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Q2.

Expert-verifiedFound in: Page 73

Book edition
Common Core Edition

Author(s)
Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages
183 pages

ISBN
9780547587776

**Are $2(x+1)\u200a\u200a\text{and}\u200a\u200a2x+1$ equivalent variable expressions? Explain.**

The two expressions are not same & they are not equivalent

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

Suppose a, b, and c is three real numbers.

**Distributive Property of Multiplication **

Property: $\text{a}\u200a\u200a\text{(b}\u200a\u200a\text{+}\u200a\u200a\text{c}\u200a\u200a\text{)}\u200a\u200a=\u200a\u200a\text{a}\u200a\u200a\xb7\u200a\u200a\text{b}\u200a\u200a+\u200a\text{a}\u200a\u200a\xb7\u200a\u200a\text{c}\u200a\u200a$

Example: $12\u200a\text{(3}\u200a\u200a\text{+}\u200a\u200a\text{4}\u200a\u200a\text{)}\u200a\u200a12=\u200a\u200a\text{12}\u200a\u200a\xb7\u200a\u200a\text{3}\u200a\u200a+\u200a\u200a\text{12}\u200a\u200a\xb7\u200a\u200a\text{4}\u200a\u200a=\u200a\u200a36\u200a\u200a+\u200a\u200a48\u200a\u200a=\u200a\u200a84$

**Using distributive property of multiplication **

Property: $\text{a}\u200a\u200a\text{(b}\u200a\u200a\text{+}\u200a\u200a\text{c}\u200a\u200a\text{)}\u200a\u200a=\u200a\u200a\text{a}\u200a\u200a\xb7\u200a\u200a\text{b}\u200a\u200a+\u200a\text{a}\u200a\u200a\xb7\u200a\u200a\text{c}\u200a\u200a$

We can write by using distributive method of multiplication: $2\left(x+1\right)$ = $2x+2$

The second expression is $2\left(x+1\right)$

Since this two expressions are not same & they are not equivalent.

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