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2. Exponents & Scientific Notation
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United States of AmericaFL
Grade 8

2.06 The distributive property with algebraic terms

Lesson
Worksheet
Practice
Worksheet
The distributive property
1

A student incorrectly used the distributive property and wrote 7 \left( 4 x + 3\right) = 28 x + 3.

Explain how to correct the error.

2

In the equation 2 \left(s + 9\right) = 2 s + 9, the distributive property has been incorrectly applied.

Write the correct right hand side of this equation.

3

Distribute the following expressions:

a
4 \left(t + 6\right)
b
3 \left(6 + r\right)
c
\left(r + 3\right) \times 5
d
- 9 \left(r + 7\right)
e
- 6 \left(n - 4\right)
f
- \left( 5 - a \right)
g
- 9 \left(5 + 4 c\right)
h
- 8 \left( - 9 n - 5\right)
i
3 r \left( 9 s - 4\right)
j
7 u \left( 8 v - 3 w\right)
k
- m \left( 2 n - 15 p\right)
l
r \left(r + 5\right)
m
y \left(y - 9\right)
n
- m \left(m + 1\right)
o
t \left( 2 t - 14\right)
p
2 n \left(n - 14\right)
4

Distribute the following expressions:

a
- \left( 3 u + 5 a - 7 t \right)
b
- 4 \left( 4 p - 3 q + 4 n\right)
c
2 m \left( 3 n - 5 p + 7\right)
d

4 p \left( 4 q - 3 + 6 r\right)

e
2 f \left(f - 8 g - 7 h\right)
f
6 a \left(a - 5 b + 3 c\right)
g
\left( 5 x + 9 y - 2\right) \left( 4 x\right)
h
2a^2\left(a^2+4a-7\right)
5

Distribute the following expressions:

a
\dfrac{1}{2} \left( 6 n + 8\right)
b
- 15 \left(\dfrac{v}{5} + 4\right)
c
-\dfrac{u}{2}\left(3a - 5t + 9\right)
d
11 \left(\dfrac{m}{14} - 2 n + \dfrac{1}{5}\right)
6

Distribute and simplify:

a

5 + 3 \left(x + 4\right)

b

8 \left( 3 x + 4\right) - 6 x

c
6 \left(y + 8\right) - 5 y - 3
d
2 x + 10 + 6 \left(x + 4\right)
e
3 x + 8 + 2 \left( 6 x + 2\right)
f
9 x - 2 - 3 \left(x + 4\right)
g
5 + 8 y \left(y + 6\right) - 4 y^{2}
h
8 u \left( 10 u + v\right) - 5
7

Distribute and simplify:

a

7 \left(y + 9\right) + 5 \left(y + 6\right)

b

x \left(x + 4\right) + 8 \left(x + 9\right)

c
6 \left( 10 x + 8 y\right) - 6 \left( - 6 y - 6 x\right)
d
2 u \left( 3 u + 5 v\right) - u \left( 6 u + v\right)
e
5 w y \left(y + w\right) + 4 w y \left(y + 2\right)
f
6 p \left( 3 q r - 3\right) - \left( 4 p q r - 5 p\right)
g

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

h

9w\left(8w+6z\right)-5w\left(4z+2w\right)

8

Complete the following statements:

a
3\left(2x+⬚\right)=⬚x+12
b
⬚\left(⬚s+5\right)=-8s+10
c
⬚\left(3g-⬚\right)=-6g+14
d
5\left(⬚p+⬚\right)=15p-30
Applications
9

A solar energy company offers a range of solar panels, each with a power rating of \\( m + 14 ) megawatts, where m is the panel model number. Write an expression in terms of m for the total amount of power produced by 9 solar panels.

10

The representatives of 8 countries are attending a global summit, and each country is able to send (3 u + 4) representatives. Write an expression for the total number of representatives attending the summit.

11

A forklift operator has enough time to make 5 trips between the two ends of a warehouse. A forklift can carry (2 + 3 n^{4}) boxes at a time. Write an expression for the total number of boxes that can be carried across the warehouse.

12

Consider the rectangle shown:

a

State the areas of the two smaller rectangles, A and B.

b

Write an expression for the area of the larger rectangle using your answer in part (a).

c

Write an expression for the area of the larger rectangle using the given base length, m + n.

d

Relate your answer in parts (b) and (c) using an equation.

13

Consider the rectangle shown:

Form an expression for the area of the rectangle in distributed form.

14

A rectangle is 8 \text{ ft} longer than it is width. Its width is represented by the variable u.

Write an expression for the area of the rectangle in distributed form.

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Outcomes

MA.8.AR.1.2

Apply properties of operations to multiply two linear expressions with rational coefficients.

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