# Lesson 11

The Distributive Property, Part 3

Let's practice writing equivalent expressions by using the distributive property.

### Problem 1

For each expression, use the distributive property to write an equivalent expression.

1. $$4(x+2)$$
2. $$(6+8)\boldcdot x$$
3. $$4(2x+3)$$
4. $$6(x+y+z)$$

### Problem 2

Priya rewrites the expression $$8y - 24$$ as $$8(y-3)$$. Han rewrites $$8y-24$$ as $$2(4y-12)$$. Are Priya's and Han's expressions each equivalent to $$8y-24$$? Explain your reasoning.

### Problem 3

Select all the expressions that are equivalent to $$16x + 36$$.

A:

$$16(x+20)$$

B:

$$x(16+36)$$

C:

$$4(4x+9)$$

D:

$$2(8x+18)$$

E:

$$2(8x+36)$$

### Problem 4

The area of a rectangle is $$30 + 12x$$. List at least 3 possibilities for the length and width of the rectangle.

### Problem 5

Select all the expressions that are equivalent to $$\frac{1}{2}z$$.

A:

$$z + z$$

B:

$$z \div 2$$

C:

$$z \boldcdot z$$

D:

$$\frac{1}{4}z + \frac{1}{4} z$$

E:

$$2z$$

(From Unit 6, Lesson 8.)

### Problem 6

1. What is the perimeter of a square with side length:

3 cm?

7 cm?

$$s$$ cm?

2. If the perimeter of a square is 360 cm, what is its side length?
3. What is the area of a square with side length:

3 cm?

7 cm?

$$s$$ cm?

4. If the area of a square is 121 cm2, what is its side length?
(From Unit 6, Lesson 6.)

### Problem 7

Solve each equation.

$$10=4a$$

$$5b=17.5$$

$$1.036=10c$$

$$0.6d=1.8$$

$$15=0.1e$$

(From Unit 6, Lesson 5.)