Lesson 11: The Distributive Property, Part 3

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

11.1: The Shaded Region

A rectangle with dimensions 6 cm and $w$ cm is partitioned into two smaller rectangles.

Explain why each of these expressions represents the area, in cm2, of the shaded portion.

  • $6w-24$
  • $6(w-4)$

11.2: Matching to Practice Distributive Property

Match each expression in column 1 to an equivalent expression in column 2. If you get stuck, consider drawing a diagram.

Column 1

  1. $a(1+2+3)$
  2. $2(12-4)$
  3. $12a+3b$
  4. $\frac23(15a-18)$
  5. $6a+10b$
  6. $0.4(5-2.5a)$
  7. $2a+3a$

Column 2

  1. $3(4a+b)$
  2. $12 \boldcdot 2 - 4 \boldcdot 2$
  3. $2(3a+5b)$
  4. $(2+3)a$
  5. $a+2a+3a$
  6. $10a-12$
  7. $2-a$

11.3: Writing Equivalent Expressions Using the Distributive Property

The distributive property can be used to write equivalent expressions. In each row, use the distributive property to write an equivalent expression. If you get stuck, draw a diagram.

  product sum or difference
row 1 $3(3+x)$  
row 2   $4x-20$
row 3 $(9-5)x$  
row 4   $4x+7x$
row 5 $3(2x+1)$  
row 6   $10x-5$
row 7   $x+2x+3x$
row 8 $\frac12 (x-6)$  
row 9 $y(3x+4z)$  
row 10   $2xyz-3yz+4xz$


The distributive property can be used to write a sum as a product, or write a product as a sum. You can always draw a partitioned rectangle to help reason about it, but with enough practice, you should be able to apply the distributive property without making a drawing.

Here are some examples of expressions that are equivalent due to the distributive property. 

$$\begin {align} 9+18&=9(1+2)\\[10pt] 2(3x+4)&=6x+8\\[10pt] 2n+3n+n&=n(2+3+1)\\[10pt] 11b-99a&=11(b-9a)\\[10pt] k(c+d-e)&=kc+kd-ke\\ \end {align}$$

Practice Problems ▶