Question

algebra 1
using the distributive property
simplify each expression.

1. $-6(a + 8)$
2. $4(1 + 9x)$
3. $6(-5n + 7)$
4. $(9m + 10) \cdot 2$
5. $(-4 - 3n) \cdot -8$
6. $8(-b - 4)$
7. $(1 - 7n) \cdot 5$
8. $-6(x + 4)$
9. $5(3m - 6)$
10. $(-6p + 7) \cdot -4$
11. $5(b - 1)$
12. $(x + 9) \cdot 5$

name_________
date_________

Explanation:

Step1: Apply distributive property

For each expression, use $a(b+c)=ab+ac$ (or $a(b-c)=ab-ac$) to expand.
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1) $-6(a + 8)$

Step1: Distribute $-6$ to terms

$-6 \cdot a + (-6) \cdot 8$

Step2: Calculate products

$-6a - 48$

2) $4(1 + 9x)$

Step1: Distribute $4$ to terms

$4 \cdot 1 + 4 \cdot 9x$

Step2: Calculate products

$4 + 36x$

3) $6(-5n + 7)$

Step1: Distribute $6$ to terms

$6 \cdot (-5n) + 6 \cdot 7$

Step2: Calculate products

$-30n + 42$

4) $(9m + 10) \cdot 2$

Step1: Distribute $2$ to terms

$9m \cdot 2 + 10 \cdot 2$

Step2: Calculate products

$18m + 20$

5) $(-4 - 3n) \cdot -8$

Step1: Distribute $-8$ to terms

$-4 \cdot (-8) + (-3n) \cdot (-8)$

Step2: Calculate products

$32 + 24n$

6) $8(-b - 4)$

Step1: Distribute $8$ to terms

$8 \cdot (-b) + 8 \cdot (-4)$

Step2: Calculate products

$-8b - 32$

7) $(1 - 7n) \cdot 5$

Step1: Distribute $5$ to terms

$1 \cdot 5 + (-7n) \cdot 5$

Step2: Calculate products

$5 - 35n$

8) $-6(x + 4)$

Step1: Distribute $-6$ to terms

$-6 \cdot x + (-6) \cdot 4$

Step2: Calculate products

$-6x - 24$

9) $5(3m - 6)$

Step1: Distribute $5$ to terms

$5 \cdot 3m + 5 \cdot (-6)$

Step2: Calculate products

$15m - 30$

10) $(-6p + 7) \cdot -4$

Step1: Distribute $-4$ to terms

$-6p \cdot (-4) + 7 \cdot (-4)$

Step2: Calculate products

$24p - 28$

11) $5(b - 1)$

Step1: Distribute $5$ to terms

$5 \cdot b + 5 \cdot (-1)$

Step2: Calculate products

$5b - 5$

12) $(x + 9) \cdot 5$

Step1: Distribute $5$ to terms

$x \cdot 5 + 9 \cdot 5$

Step2: Calculate products

$5x + 45$

Answer:

1. $\boldsymbol{-6a - 48}$
2. $\boldsymbol{4 + 36x}$
3. $\boldsymbol{-30n + 42}$
4. $\boldsymbol{18m + 20}$
5. $\boldsymbol{32 + 24n}$
6. $\boldsymbol{-8b - 32}$
7. $\boldsymbol{5 - 35n}$
8. $\boldsymbol{-6x - 24}$
9. $\boldsymbol{15m - 30}$
10. $\boldsymbol{24p - 28}$
11. $\boldsymbol{5b - 5}$
12. $\boldsymbol{5x + 45}$