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Q42.

Expert-verified
Found in: Page 73

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Use the distributive property to evaluate the expression.$-3 \left(9-1+6\right)$

$- 3 \left( 9 - 1 + 6 \right) = - 42$.

See the step by step solution

## Step-1 – What are real numbers?

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

## Step-2 – Distributive Property of Multiplication

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

Distributive Property of Multiplication

Property: $-\text{a} \text{(b} - \text{c} \text{)} = \left(-\text{a} \right) · \text{b} - \left(-\text{a} \right) · \text{c}$

Example: $-\text{3} \text{(8} - \text{5} \text{)} = \left(-\text{3} \right) · 8 -\text{} \left(-\text{3} \right) · \text{5} = -24+15=- 9$

## Step-3:  Use the distributive property to evaluate the expression.

We know that double negative is always positive. $-3 · -1 = + 3$

Distributive Property of Multiplication

Property: $-\text{a} \text{(b} - \text{c} \text{)} = \left(-\text{a} \right) · \text{b} - \left(-\text{a} \right) · \text{c}$

$\begin{array}{l}-\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\left(\text{\hspace{0.17em}\hspace{0.17em}}9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}1\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}=-\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}\left(-\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}1\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}\left(-\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}·\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}27\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}18\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}42\\ \\ -\text{\hspace{0.17em}\hspace{0.17em}}3\text{\hspace{0.17em}\hspace{0.17em}}\left(\text{\hspace{0.17em}\hspace{0.17em}}9\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}1\text{\hspace{0.17em}\hspace{0.17em}}+\text{\hspace{0.17em}\hspace{0.17em}}6\text{\hspace{0.17em}\hspace{0.17em}}\right)\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}}42\end{array}$