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Expression Math

- Calculus
- Absolute Maxima and Minima
- Absolute and Conditional Convergence
- Accumulation Function
- Accumulation Problems
- Algebraic Functions
- Alternating Series
- Antiderivatives
- Application of Derivatives
- Approximating Areas
- Arc Length of a Curve
- Arithmetic Series
- Average Value of a Function
- Calculus of Parametric Curves
- Candidate Test
- Combining Differentiation Rules
- Combining Functions
- Continuity
- Continuity Over an Interval
- Convergence Tests
- Cost and Revenue
- Density and Center of Mass
- Derivative Functions
- Derivative of Exponential Function
- Derivative of Inverse Function
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Derivatives
- Derivatives and Continuity
- Derivatives and the Shape of a Graph
- Derivatives of Inverse Trigonometric Functions
- Derivatives of Polar Functions
- Derivatives of Sec, Csc and Cot
- Derivatives of Sin, Cos and Tan
- Determining Volumes by Slicing
- Direction Fields
- Disk Method
- Divergence Test
- Eliminating the Parameter
- Euler's Method
- Evaluating a Definite Integral
- Evaluation Theorem
- Exponential Functions
- Finding Limits
- Finding Limits of Specific Functions
- First Derivative Test
- Function Transformations
- General Solution of Differential Equation
- Geometric Series
- Growth Rate of Functions
- Higher-Order Derivatives
- Hydrostatic Pressure
- Hyperbolic Functions
- Implicit Differentiation Tangent Line
- Implicit Relations
- Improper Integrals
- Indefinite Integral
- Indeterminate Forms
- Initial Value Problem Differential Equations
- Integral Test
- Integrals of Exponential Functions
- Integrals of Motion
- Integrating Even and Odd Functions
- Integration Formula
- Integration Tables
- Integration Using Long Division
- Integration of Logarithmic Functions
- Integration using Inverse Trigonometric Functions
- Intermediate Value Theorem
- Inverse Trigonometric Functions
- Jump Discontinuity
- Lagrange Error Bound
- Limit Laws
- Limit of Vector Valued Function
- Limit of a Sequence
- Limits
- Limits at Infinity
- Limits of a Function
- Linear Approximations and Differentials
- Linear Differential Equation
- Linear Functions
- Logarithmic Differentiation
- Logarithmic Functions
- Logistic Differential Equation
- Maclaurin Series
- Manipulating Functions
- Maxima and Minima
- Maxima and Minima Problems
- Mean Value Theorem for Integrals
- Models for Population Growth
- Motion Along a Line
- Motion in Space
- Natural Logarithmic Function
- Net Change Theorem
- Newton's Method
- Nonhomogeneous Differential Equation
- One-Sided Limits
- Optimization Problems
- P Series
- Particle Model Motion
- Particular Solutions to Differential Equations
- Polar Coordinates
- Polar Coordinates Functions
- Polar Curves
- Population Change
- Power Series
- Ratio Test
- Removable Discontinuity
- Riemann Sum
- Rolle's Theorem
- Root Test
- Second Derivative Test
- Separable Equations
- Simpson's Rule
- Solid of Revolution
- Solutions to Differential Equations
- Surface Area of Revolution
- Symmetry of Functions
- Tangent Lines
- Taylor Polynomials
- Taylor Series
- Techniques of Integration
- The Fundamental Theorem of Calculus
- The Mean Value Theorem
- The Power Rule
- The Squeeze Theorem
- The Trapezoidal Rule
- Theorems of Continuity
- Trigonometric Substitution
- Vector Valued Function
- Vectors in Calculus
- Vectors in Space
- Washer Method
- Decision Maths
- Geometry
- 2 Dimensional Figures
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- 3-Dimensional Figures
- Altitude
- Angles in Circles
- Arc Measures
- Area and Volume
- Area of Circles
- Area of Circular Sector
- Area of Parallelograms
- Area of Plane Figures
- Area of Rectangles
- Area of Regular Polygons
- Area of Rhombus
- Area of Trapezoid
- Area of a Kite
- Composition
- Congruence Transformations
- Congruent Triangles
- Convexity in Polygons
- Coordinate Systems
- Dilations
- Distance and Midpoints
- Equation of Circles
- Equilateral Triangles
- Figures
- Fundamentals of Geometry
- Geometric Inequalities
- Geometric Mean
- Geometric Probability
- Glide Reflections
- HL ASA and AAS
- Identity Map
- Inscribed Angles
- Isometry
- Isosceles Triangles
- Law of Cosines
- Law of Sines
- Linear Measure and Precision
- Median
- Parallel Lines Theorem
- Parallelograms
- Perpendicular Bisector
- Plane Geometry
- Polygons
- Projections
- Properties of Chords
- Proportionality Theorems
- Pythagoras Theorem
- Rectangle
- Reflection in Geometry
- Regular Polygon
- Rhombuses
- Right Triangles
- Rotations
- SSS and SAS
- Segment Length
- Similarity
- Similarity Transformations
- Special quadrilaterals
- Squares
- Surface Area of Cone
- Surface Area of Cylinder
- Surface Area of Prism
- Surface Area of Sphere
- Surface Area of a Solid
- Surface of Pyramids
- Symmetry
- Translations
- Trapezoids
- Triangle Inequalities
- Triangles
- Using Similar Polygons
- Vector Addition
- Vector Product
- Volume of Cone
- Volume of Cylinder
- Volume of Pyramid
- Volume of Solid
- Volume of Sphere
- Volume of prisms
- Mechanics Maths
- Acceleration and Time
- Acceleration and Velocity
- Angular Speed
- Assumptions
- Calculus Kinematics
- Coefficient of Friction
- Connected Particles
- Constant Acceleration
- Constant Acceleration Equations
- Converting Units
- Force as a Vector
- Kinematics
- Newton's First Law
- Newton's Law of Gravitation
- Newton's Second Law
- Newton's Third Law
- Projectiles
- Pulleys
- Resolving Forces
- Statics and Dynamics
- Tension in Strings
- Variable Acceleration
- Probability and Statistics
- Bar Graphs
- Basic Probability
- Charts and Diagrams
- Conditional Probabilities
- Continuous and Discrete Data
- Frequency, Frequency Tables and Levels of Measurement
- Independent Events Probability
- Line Graphs
- Mean Median and Mode
- Mutually Exclusive Probabilities
- Probability Rules
- Probability of Combined Events
- Quartiles and Interquartile Range
- Systematic Listing
- Pure Maths
- ASA Theorem
- Absolute Value Equations and Inequalities
- Addition and Subtraction of Rational Expressions
- Addition, Subtraction, Multiplication and Division
- Algebra
- Algebraic Fractions
- Algebraic Notation
- Algebraic Representation
- Analyzing Graphs of Polynomials
- Angle Measure
- Angles
- Angles in Polygons
- Approximation and Estimation
- Area and Circumference of a Circle
- Area and Perimeter of Quadrilaterals
- Area of Triangles
- Arithmetic Sequences
- Average Rate of Change
- Bijective Functions
- Binomial Expansion
- Binomial Theorem
- Chain Rule
- Circle Theorems
- Circles
- Circles Maths
- Combination of Functions
- Combinatorics
- Common Factors
- Common Multiples
- Completing the Square
- Completing the Squares
- Complex Numbers
- Composite Functions
- Composition of Functions
- Compound Interest
- Compound Units
- Conic Sections
- Construction and Loci
- Converting Metrics
- Convexity and Concavity
- Coordinate Geometry
- Coordinates in Four Quadrants
- Cubic Function Graph
- Cubic Polynomial Graphs
- Data transformations
- Deductive Reasoning
- Definite Integrals
- Deriving Equations
- Determinant of Inverse Matrix
- Determinants
- Differential Equations
- Differentiation
- Differentiation Rules
- Differentiation from First Principles
- Differentiation of Hyperbolic Functions
- Direct and Inverse proportions
- Disjoint and Overlapping Events
- Disproof by Counterexample
- Distance from a Point to a Line
- Divisibility Tests
- Double Angle and Half Angle Formulas
- Drawing Conclusions from Examples
- Ellipse
- Equation of Line in 3D
- Equation of a Perpendicular Bisector
- Equation of a circle
- Equations
- Equations and Identities
- Equations and Inequalities
- Estimation in Real Life
- Euclidean Algorithm
- Evaluating and Graphing Polynomials
- Even Functions
- Exponential Form of Complex Numbers
- Exponential Rules
- Exponentials and Logarithms
- Expression Math
- Expressions and Formulas
- Faces Edges and Vertices
- Factorials
- Factoring Polynomials
- Factoring Quadratic Equations
- Factorising expressions
- Factors
- Finding Maxima and Minima Using Derivatives
- Finding Rational Zeros
- Finding the Area
- Forms of Quadratic Functions
- Fractional Powers
- Fractional Ratio
- Fractions
- Fractions and Decimals
- Fractions and Factors
- Fractions in Expressions and Equations
- Fractions, Decimals and Percentages
- Function Basics
- Functional Analysis
- Functions
- Fundamental Counting Principle
- Fundamental Theorem of Algebra
- Generating Terms of a Sequence
- Geometric Sequence
- Gradient and Intercept
- Graphical Representation
- Graphing Rational Functions
- Graphing Trigonometric Functions
- Graphs
- Graphs and Differentiation
- Graphs of Common Functions
- Graphs of Exponents and Logarithms
- Graphs of Trigonometric Functions
- Greatest Common Divisor
- Growth and Decay
- Growth of Functions
- Highest Common Factor
- Hyperbolas
- Imaginary Unit and Polar Bijection
- Implicit differentiation
- Inductive Reasoning
- Inequalities Maths
- Infinite geometric series
- Injective functions
- Instantaneous Rate of Change
- Integers
- Integrating Polynomials
- Integrating Trig Functions
- Integrating e^x and 1/x
- Integration
- Integration Using Partial Fractions
- Integration by Parts
- Integration by Substitution
- Integration of Hyperbolic Functions
- Interest
- Inverse Hyperbolic Functions
- Inverse Matrices
- Inverse and Joint Variation
- Inverse functions
- Iterative Methods
- Law of Cosines in Algebra
- Law of Sines in Algebra
- Laws of Logs
- Limits of Accuracy
- Linear Expressions
- Linear Systems
- Linear Transformations of Matrices
- Location of Roots
- Logarithm Base
- Logic
- Lower and Upper Bounds
- Lowest Common Denominator
- Lowest Common Multiple
- Math formula
- Matrices
- Matrix Addition and Subtraction
- Matrix Determinant
- Matrix Multiplication
- Metric and Imperial Units
- Misleading Graphs
- Mixed Expressions
- Modulus Functions
- Modulus and Phase
- Multiples of Pi
- Multiplication and Division of Fractions
- Multiplicative Relationship
- Multiplying and Dividing Rational Expressions
- Natural Logarithm
- Natural Numbers
- Notation
- Number
- Number Line
- Number Systems
- Numerical Methods
- Odd functions
- Open Sentences and Identities
- Operation with Complex Numbers
- Operations with Decimals
- Operations with Matrices
- Operations with Polynomials
- Order of Operations
- Parabola
- Parallel Lines
- Parametric Differentiation
- Parametric Equations
- Parametric Integration
- Partial Fractions
- Pascal's Triangle
- Percentage
- Percentage Increase and Decrease
- Percentage as fraction or decimals
- Perimeter of a Triangle
- Permutations and Combinations
- Perpendicular Lines
- Points Lines and Planes
- Polynomial Graphs
- Polynomials
- Powers Roots And Radicals
- Powers and Exponents
- Powers and Roots
- Prime Factorization
- Prime Numbers
- Problem-solving Models and Strategies
- Product Rule
- Proof
- Proof and Mathematical Induction
- Proof by Contradiction
- Proof by Deduction
- Proof by Exhaustion
- Proof by Induction
- Properties of Exponents
- Proportion
- Proving an Identity
- Pythagorean Identities
- Quadratic Equations
- Quadratic Function Graphs
- Quadratic Graphs
- Quadratic functions
- Quadrilaterals
- Quotient Rule
- Radians
- Radical Functions
- Rates of Change
- Ratio
- Ratio Fractions
- Rational Exponents
- Rational Expressions
- Rational Functions
- Rational Numbers and Fractions
- Ratios as Fractions
- Real Numbers
- Reciprocal Graphs
- Recurrence Relation
- Recursion and Special Sequences
- Remainder and Factor Theorems
- Representation of Complex Numbers
- Rewriting Formulas and Equations
- Roots of Complex Numbers
- Roots of Polynomials
- Rounding
- SAS Theorem
- SSS Theorem
- Scalar Triple Product
- Scale Drawings and Maps
- Scale Factors
- Scientific Notation
- Second Order Recurrence Relation
- Sector of a Circle
- Segment of a Circle
- Sequences
- Sequences and Series
- Series Maths
- Sets Math
- Similar Triangles
- Similar and Congruent Shapes
- Simple Interest
- Simplifying Fractions
- Simplifying Radicals
- Simultaneous Equations
- Sine and Cosine Rules
- Small Angle Approximation
- Solving Linear Equations
- Solving Linear Systems
- Solving Quadratic Equations
- Solving Radical Inequalities
- Solving Rational Equations
- Solving Simultaneous Equations Using Matrices
- Solving Systems of Inequalities
- Solving Trigonometric Equations
- Solving and Graphing Quadratic Equations
- Solving and Graphing Quadratic Inequalities
- Special Products
- Standard Form
- Standard Integrals
- Standard Unit
- Straight Line Graphs
- Substraction and addition of fractions
- Sum and Difference of Angles Formulas
- Sum of Natural Numbers
- Surds
- Surjective functions
- Tables and Graphs
- Tangent of a Circle
- The Quadratic Formula and the Discriminant
- Transformations
- Transformations of Graphs
- Translations of Trigonometric Functions
- Triangle Rules
- Triangle trigonometry
- Trigonometric Functions
- Trigonometric Functions of General Angles
- Trigonometric Identities
- Trigonometric Ratios
- Trigonometry
- Turning Points
- Types of Functions
- Types of Numbers
- Types of Triangles
- Unit Circle
- Units
- Variables in Algebra
- Vectors
- Verifying Trigonometric Identities
- Writing Equations
- Writing Linear Equations
- Statistics
- Bias in Experiments
- Binomial Distribution
- Binomial Hypothesis Test
- Bivariate Data
- Box Plots
- Categorical Data
- Categorical Variables
- Central Limit Theorem
- Chi Square Test for Goodness of Fit
- Chi Square Test for Homogeneity
- Chi Square Test for Independence
- Chi-Square Distribution
- Combining Random Variables
- Comparing Data
- Comparing Two Means Hypothesis Testing
- Conditional Probability
- Conducting a Study
- Conducting a Survey
- Conducting an Experiment
- Confidence Interval for Population Mean
- Confidence Interval for Population Proportion
- Confidence Interval for Slope of Regression Line
- Confidence Interval for the Difference of Two Means
- Confidence Intervals
- Correlation Math
- Cumulative Frequency
- Data Analysis
- Data Interpretation
- Discrete Random Variable
- Distributions
- Dot Plot
- Empirical Rule
- Errors in Hypothesis Testing
- Events (Probability)
- Frequency Polygons
- Generalization and Conclusions
- Geometric Distribution
- Histograms
- Hypothesis Test for Correlation
- Hypothesis Test of Two Population Proportions
- Hypothesis Testing
- Inference for Distributions of Categorical Data
- Inferences in Statistics
- Large Data Set
- Least Squares Linear Regression
- Linear Interpolation
- Linear Regression
- Measures of Central Tendency
- Methods of Data Collection
- Normal Distribution
- Normal Distribution Hypothesis Test
- Normal Distribution Percentile
- Point Estimation
- Probability
- Probability Calculations
- Probability Distribution
- Probability Generating Function
- Quantitative Variables
- Quartiles
- Random Variables
- Randomized Block Design
- Residuals
- Sample Mean
- Sample Proportion
- Sampling
- Sampling Distribution
- Scatter Graphs
- Single Variable Data
- Standard Deviation
- Standard Normal Distribution
- Statistical Graphs
- Statistical Measures
- Stem and Leaf Graph
- Survey Bias
- Transforming Random Variables
- Tree Diagram
- Two Categorical Variables
- Two Quantitative Variables
- Type I Error
- Type II Error
- Types of Data in Statistics
- Venn Diagrams

Any real-life scenario containing unknown quantities can be modelled into mathematical statements. For instance, say you wanted to model the population of eagles and frogs in a particular habitat. Each year, the population of frogs double while the population of eagles halves. By creating a suitable expression that describes the decrease of eagles and the increase of frogs in this ecosystem, we can make predictions and identify trends in their population.

In this article, we will discuss expressions, what they look like, and how to factorise and simplify them.

An expression can be used to describe a scenario when an **unknown number** is present or when a **variable** value exists. It helps solve real-world problems in a more simplified and explicit manner.

A variable value is a value that changes over time.

To construct an expression of this kind, you would need to determine which quantity is unknown in the circumstance, and then define a variable to represent it. Before we dive into this topic further, let us first define expressions.

**Expressions **are mathematical statements that have two terms at least that contain variables, numbers, or both. Expressions are such that they contain also at least, one mathematical operation; addition, subtraction, multiplication, and division.

Let's see an example of an expression.

The following is a mathematical expression,

\[2x+1\]

because it contains one variable, \(x\), two numbers, 2 and 1, and one mathematical operation, +.

Expressions are very organised, in a way that a statement that has an operator come right after another one is not a valid expression. For example,

\[2x+\times 1.\]

They are also organised in the sense that when a parenthesis opens, there needs to be a close. For example,

\[3(4x+2)-6\]

is a valid expression. However,

\[6-4(18x\]

is not a valid expression.

Expressions in algebra contain at least a variable, numbers, and an arithmetic operation. However, there are quite a number of terms related to the parts of an expression. These elements are described below.

**Variables**: Variables are the letters that represent an unknown value in a mathematical statement.**Terms**: Terms are either numbers or variables (or numbers and variables) multiplying and dividing each other and are separated by either the addition (+) or subtraction sign (-).**Coefficient**: Coefficients are the numbers that multiply variables.**Constant**: Constants are the numbers in expressions that do not change.

Components of an expression

Here are some examples of mathematical expressions.

1) \((x+1)(x+3)\)

2) \(6a+3\)

3) \(6x-15y+12\)

4) \(y^2+4xy\)

5) \(\frac{x}{4}+\frac{x}{5}\)

Notice that all of them contain the necessary components to be considered expressions. They all have variables, numbers, and at least one mathematical operation composing them.

In particular, in the first example, you will find a multiplication implicit in the parenthesis that connects the two terms \(x+1\) and \(x+3\); so it is a valid expression. In the fourth example, in the second term, variables \(x\) and \(y\) are multiplying and it's written as \(xy\). So, that one is also a valid expression.

In this segment of our discussion, we will be introduced to writing expressions, particularly translating word problems into mathematical ones. Such skill is important when solving a given question. By doing so, we can visualise anything in terms of numbers and arithmetic operations!

Given a sentence that illustrates a mathematical statement, we can translate them into expressions that involve the appropriate components of expressions we had mentioned before and mathematical symbols. The table below demonstrates several examples of word problems that have been translated into expressions.

Phrase | Expression |

Five more than a number | \[x+5\] |

Three-fourths of a number | \[\frac{3y}{4}\] |

Eight larger than a number | \[a+8\] |

The product of a number with twelve | \[12z\] |

The quotient of a number and nine | \[\frac{x}{9}\] |

In comparison to what expressions are, there are expressions that do not contain variables. These are called numerical expressions.

**Numerical expressions **are a combination of numbers with mathematical operators separating them.

They could be as long as possible, containing as many mathematical operators as possible also.

Here are a few examples of numerical expressions.

1) \(13-3\)

2) \(3-7+14-9\)

3) \(12+\frac{4}{17}-2\times 11+1\)

4) \(4-2-1\)

Algebraic expressions are expressions that contain unknowns. **Unknowns** are variables that are often represented by letters. In most cases throughout our syllabus, these letters are \(x\), \(y\) and \(z\).

However, we may sometimes get expressions that comprise Greek letters as well. For instance, \(\alpha\), \(\beta\) and \(\gamma\). Below are several examples of algebraic expressions.

1) \(\frac{2x}{7}+3y^2\)

2) \(4\alpha-3\beta + 15\)

3) \(x^2+3y-4z\)

In this section, we will be introduced to evaluating math expression. Here, we would essentially solve a given expression based on the arithmetic operations between the numbers or variables. These basic arithmetic operations (or mathematical symbols) include addition, subtraction, multiplication and division. We will also see how these operations can help us factorise and simplify such expressions.

Addition and subtraction are the primary actions done when adding and subtracting fractions. These are performed on like terms. There are two steps to consider here, namely

**Step 1:**Identify and rearrange like terms to be grouped.**Step 2:**Add and subtract like terms.

Below is a worked example.

Add the expressions \(5a-7b+3c\) and \(-4a-2b+3c\).

**Solution**

**Step 1:** We will first put the two expressions together so we can rearrange them.

\[5a-7b+3c+(-4a-2b+3c)\]

Then,

\[5a-7b+3c-4a-2b+3c\]

Next,

\[5a-4a-7b-2b+3c+3c\]

**Step 2:** We can now successfully add all the like terms.

\[a-9b+6c\]

Here is another worked example for you.

Add the expressions

\(7x^2+8y-9y\), \(3y+2-3x^2\) and \(3-y+3x^2\).

**Solution**

**Step 1:** We will note them down so that they can be rearranged

\[7x^2+8y-9+3y+2-3x^2+3-y+3x^2\]

Then,

\[7x^2+3x^2-3x^2+8y-y+3y-9+2+3\]

**Step 2:** Add the like terms

\[7x^2+10y-4\]

This is an important element when it comes to dealing with expressions. It helps us group like terms in order for us to perform arithmetic operations more structured manner.

**Factorising **is the process of reversing the expansion of brackets.

The factorised form of expressions is always in brackets. The process involves taking out the highest common factors (HCF) from all the terms such that when the factors are taken out and multiplied by the values in the brackets, we will arrive at the same expression we had in the first place.

For example, say you had the expression below.

\[4x^2+6x\]

Notice here that the coefficients of \(x^2\) and \(x\) both have a factor of 2 since 4 and 6 are divisible by 2. Furthermore, \(x^2\) and \(x\) have a common factor of \(x\). Thus, you can take these two factors out of this expression, making the factories form equivalent to

\[2x(2x+3)\]

Let's explain this again with another example.

Factorise the expression

\[6x+9\]

**Solution**

To factorise this we need to find the HCF of \(6x\) and 9. That value happens to be 3. Therefore, we will note down the value and account for the bracket.

\[3(?+?)\]

The sign in the bracket above is gotten from the sign in the initial expression. To find out what values must be in the brackets, we will divide the terms in the expressions that we factorised the 3 from by the 3.

\[\frac{6x}{3}=2x\]

and

\[\frac{9}{3}=3\]

Then, we will arrive at

\[3(2x+3)\]

We can evaluate to see if the answer we have is right by expanding the brackets.

\[(3\times 2x)+(3\times 3)=6x+9\]

as we had before!

Let's go through one more example.

Simplify the expression

\[3y^2+12y\]

**Solution**

We will need to find the HCF. Usually, these can be broken down just if they are a bit too complex at first. Looking at the coefficients, we realise that 3 is the HCF. That will be taken outside the bracket.

\[3(?+?)\]

We can now divide the expression from which the 3 was factored by the 3.

\[\frac{3y^2}{3}=y^2\]

and

\[\frac{12y}{3}=4y\]

This leaves us with the expression;

\[3(y^2+4y)\]

However, carefully looking at the expression, we will notice that this can be factored further. \(y\) can be factored out of the expression in the bracket.

\[3y(?+?)\]

We will go over the process again by dividing the values that y has been factored from by \(y\).

\[\frac{y^2}{y}=y\]

and

\[\frac{4y}{y}=4\]

This leaves us with the final expression in its factored form;

\[3y(y+4)\]

We can evaluate this by expanding the brackets.

\[(3y\times y)+(3y\times 4)=3y^2+12y\]

which again, is what we had at the beginning.

The term simplifying stems from the root word "simple". As the word suggests, simplifying a given expression allows us to solve them more efficiently. When we simplify an expression, we are reducing it into a simpler form by cancelling common factors and regrouping terms that share the same variable.

**Simplifying expressions** is the process of writing expressions in their most compact and simplest forms such that the value of the original expression is maintained.

This avoids all the lengthy working you might have to perform that may result in unwanted careless mistakes. Surely, you wouldn't want to have any arithmetic errors now, would you?

There are three steps to follow when simplifying expressions.

Eliminate the brackets by multiplying out the factors (if any are present);

Remove exponents by using the exponent rules;

Add and subtract like terms.

Let's go through some worked examples.

Simplify the expression

\[3x+2(x-4).\]

**Solution**

Here, we will first operate on the brackets by multiplying the factor (outside the bracket) by what is in the brackets.

\[3x+2x-8\]

We will add like terms, which will give us our simplified form as

\[5x-8\]

which indeed holds the same value as the expression we had in the beginning.

Here is another example.

Simplify the expression

\[x(4-x)-x(3-x).\]

**Solution**

With this problem, we will deal with the brackets first. We will multiply the factors by elements of the brackets.

\[x(4-x)-x(3-x)\]

This yields,

\[4x-x^2-3x+x^2\]

We can go ahead here to rearrange them such that like terms are grouped close together.

\[4x-3x-x^2+x^2\]

Let us now do the additions and subtractions, which will in turn leave us with:

\[4x-3x-x^2+x^2=x\]

- Expressions are mathematical statements that have two terms at least that contain variables, numbers, or both.
- Terms are either numbers or variables or numbers and variables multiplying each other.
- Numerical expressions are a combination of numbers with mathematical operators separating them.
- Factorising is the process of reversing the expansion of brackets.
- The factorising process involves taking out the highest common factors (HCF) from all the terms such that when the factors are taken out and multiplied by the values in the brackets, we will arrive at the same expression we had in the first place.
- Simplifying expressions is the process of writing expressions in their most compact and simplest forms such that the value of the original expression is maintained.

- 2x+1
- 3x+5y-8
- 6a-3

The steps to simplify expressions are

- Eliminate the brackets by multiplying the factors if there are any.
- Also, remove exponents by using the exponent rules.
- Add and subtract the like terms.

More about Expression Math

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