7.3 Distributive Property

Before you get started, take this readiness quiz.

Multiply: $3 \left(0.25\right) .$
If you missed this problem, review the reference

Simplify: $10 - \left(−2\right) \left(3\right) .$
If you missed this problem, review the reference

Combine like terms: $9 y + 17 + 3 y - 2 .$
If you missed this problem, review the reference.

Simplify: $3 \left(x + 4\right) .$

Simplify: $4 \left(x + 2\right) .$

Simplify: $6 \left(x + 7\right) .$

Simplify: $9 \left(3 y + 8\right) .$

Simplify: $5 \left(5 w + 9\right) .$

Simplify: $7 \left(x - 6\right) .$

Simplify: $8 \left(x - 5\right) .$

Simplify: $\frac{2}{5} \left(p + 10\right) .$

Simplify: $\frac{3}{7} \left(u + 21\right) .$

Simplify: $6 \left(\frac{5}{6} y + \frac{1}{2}\right) .$

Simplify: $12 \left(\frac{1}{3} n + \frac{3}{4}\right) .$

Simplify: $100 \left(0.7 + 0.15 p\right) .$

Simplify: $100 \left(0.04 + 0.35 d\right) .$

Simplify: $r \left(s - 2\right) .$

Simplify: $y \left(z - 8\right) .$

Simplify: $\left(x + 2\right) p .$

Simplify: $\left(y + 4\right) q .$

Simplify: $−3 \left(6 m + 5\right) .$

Simplify: $−6 \left(8 n + 11\right) .$

Simplify: $−5 \left(2 - 3 a\right) .$

Simplify: $−7 \left(8 - 15 y\right) .$

Simplify: $- \left(z - 11\right) .$

Simplify: $- \left(x - 4\right) .$

Simplify: $9 - 3 \left(x + 2\right) .$

Simplify: $7 x - 5 \left(x + 4\right) .$

Simplify: $6 \left(x - 9\right) - \left(x + 12\right) .$

Simplify: $8 \left(x - 1\right) - \left(x + 5\right) .$

Evaluate when $w = 3 :$ⓐ $5 \left(5 w + 9\right)$ⓑ $5 \cdot 5 w + 5 \cdot 9 .$

Evaluate when $y = 2 :$ⓐ $9 \left(3 y + 8\right)$ⓑ $9 \cdot 3 y + 9 \cdot 8 .$

Evaluate when $n = −2 :$ⓐ $−6 \left(8 n + 11\right)$ⓑ $−6 \cdot 8 n + \left(−6\right) \cdot 11 .$

Evaluate when $m = −1 :$ⓐ $−3 \left(6 m + 5\right)$ⓑ $−3 \cdot 6 m + \left(−3\right) \cdot 5 .$

Evaluate when $x = 36 :$ⓐ $- \left(x - 4\right)$ⓑ $- x + 4$ to show that $- \left(x - 4\right) = - x + 4 .$

Evaluate when $z = 55 :$ⓐ $- \left(z - 10\right)$ⓑ $- z + 10$ to show that $- \left(z - 10\right) = - z + 10 .$

Simplify using the distributive property.

$3 \left(a + 9\right)$

Simplify using the distributive property.

$9 \left(3 w + 7\right)$

Simplify using the distributive property.

$7 \left(y - 13\right)$

Simplify using the distributive property.

$5 \left(7 u - 4\right)$

Simplify using the distributive property.

$\frac{1}{3} \left(u + 9\right)$

Simplify using the distributive property.

$\frac{1}{5} \left(4 m + 20\right)$

Simplify using the distributive property.

$10 \left(\frac{3}{10} x - \frac{2}{5}\right)$

Simplify using the distributive property.

$12 \left(\frac{1}{6} + \frac{3}{4} s\right)$

Simplify using the distributive property.

$u \left(v - 10\right)$

Simplify using the distributive property.

$\left(a + 7\right) x$

Simplify using the distributive property.

$−3 \left(a + 11\right)$

Simplify using the distributive property.

$−9 \left(9 a + 4\right)$

Simplify using the distributive property.

$−4 \left(q - 7\right)$

Simplify using the distributive property.

$−6 \left(7 x - 8\right)$

Simplify using the distributive property.

$- \left(q + 11\right)$

Simplify using the distributive property.

$- \left(5 p - 4\right)$

Simplify using the distributive property.

$12 + 8 \left(u - 1\right)$

Simplify using the distributive property.

$18 - 4 \left(x + 2\right)$

Simplify using the distributive property.

$9 - 6 \left(7 n - 5\right)$

Simplify using the distributive property.

$8 - \left(r - 7\right)$

Simplify using the distributive property.

$−4 - \left(c - 10\right)$

Simplify using the distributive property.

$\left(4 y - 1\right) - \left(y - 2\right)$

Simplify using the distributive property.

$9 \left(5 u + 8\right) + 2 \left(u - 6\right)$

Simplify using the distributive property.

$4 \left(6 x - 1\right) - \left(−8\right)$

Simplify using the distributive property.

$11 \left(n - 7\right) - 5 \left(n - 1\right)$

Simplify using the distributive property.

$7 \left(3 n + 9\right) - \left(4 n - 13\right)$

Evaluate both expressions for the given value.

If $u = −1 ,$ evaluate

1. ⓐ $8 \left(5 u + 12\right)$
2. ⓑ $8 \cdot 5 u + 8 \cdot 12$

Evaluate both expressions for the given value.

If $y = \frac{3}{4} ,$ evaluate

1. ⓐ $4 \left(y + \frac{3}{8}\right)$
2. ⓑ $4 \cdot y + 4 \cdot \frac{3}{8}$

Evaluate both expressions for the given value.

If $p = \frac{23}{30} ,$ evaluate

1. ⓐ $−6 \left(5 p + 11\right)$
2. ⓑ $−6 \cdot 5 p + \left(−6\right) \cdot 11$

Evaluate both expressions for the given value.

If $n = 0.75 ,$ evaluate

1. ⓐ $−100 \left(5 n + 1.5\right)$
2. ⓑ $−100 \cdot 5 n + \left(−100\right) \left(1.5\right)$

Evaluate both expressions for the given value.

If $w = −80 ,$ evaluate

1. ⓐ $- \left(w - 80\right)$
2. ⓑ $- w + 80$

Evaluate both expressions for the given value.

If $q = 0.55 ,$ evaluate

1. ⓐ $- \left(q + 0.48\right)$
2. ⓑ $- q - 0.48$

Multi-pack purchase Adele’s shampoo sells for $\$\text{3}.\text{97}$ per bottle at the drug store. At the warehouse store, the same shampoo is sold as a $\text{3}-\text{pack}$ for $\$\text{10}.\text{49} .$

1. ⓐ Show how you can use the distributive property to find the cost of $3$ bottles bought individually at the drug store.

2. ⓑ How much would Adele save by buying the $\text{3}-\text{pack}$ at the warehouse store?

Explain how you can multiply $4 \left(\$\text{5}.\text{97}\right)$ without paper or a calculator by thinking of $\$\text{5}.\text{97}$ as $6 - 0.03$ and then using the distributive property.