Middle Years

# 2.04 Expansion

Worksheet
The distributive law
1

A student incorrectly used the distributive property and wrote 6 \left( 7 x + 2\right) = 42 x + 2.

Explain how to correct the error.

2

Expand the following expressions:

a

5 \left(s + 7\right)

b

9 \left(5 + w\right)

c

3 \left(r - 6\right)

d

\left(y + 8\right) \times 7

e

- 8 \left(t + 10\right)

f

- 8 \left(c - 5\right)

g

- \left( y + 2 \right)

h

4 \left( 4 s + 5\right)

i

- 10 \left(8 + 3 r\right)

j

- 8 \left( - 2 t - 3\right)

k

p \left(q + 4\right)

l

9 \left(u - v\right)

m

- \left( 2 m - 3 n \right)

n

- r \left( 11 s + 13 t\right)

o

4 \left( 2 r + 3 s + 5 t\right)

p

6\left(4m+3n+5p\right)

3

Expand the following expressions:

a

6 m \left( 2 n + 3\right)

b

9 \left(v^{2} + 6\right)

c

r \left(r + 7\right)

d

6 m \left( 4 m + 7\right)

e

- 6 a \left( 2 a + 9\right)

f

4 w y \left(y + w\right)

g

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

h

2 f \left(f - 7 g - 6 h\right)

i

- 10 \left(y^{2} + 7\right)

j

- \left( 9 - s^{3} \right)

k

r \left(s^{2} + 8\right)

l

- 10 \left(3 + 8 u^{3}\right)

m

4 s^{5} \left( 4 t^{4} - 9\right)

n

6p^3\left(2q^5-9\right)

o

9f\left(f-4g-6h\right)

p

3uv\left(v+u\right)

4

Expand and simplify the following expressions:

a

4 \left(x + 8\right) - 2

b

7 + 5 \left( 3 x + 4\right)

c

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

d

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

e

34 + 9 \left( 4 x - 5\right)

f

5 x - 8 \left( 2 x - 3\right)

g

9 x - 5 \left( 2 x + 3\right)

h

- 8 \left( 5 x - 7\right) - 9

i

4 y + 5 + 6 \left(y - 9\right)

j

4 \left( 5 \left(x - 3\right) + 2\right)

5

Expand and simplify the following expressions:

a

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

b

8 y^{2} - 4 y + 7 y \left(y - 5\right)

c

3 \left( 6 x - 5 y\right) - 2 \left( 9 y + 4 x\right)

d

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

e

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

f

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

g

-8 \left(x + 4\right) - 3 \left(x - 2\right)

h

11\left(a + 4\right) -6 \left(4-a \right)

i

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

j

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

Applications
6

A solar energy company offers a range of solar panels, each with a power rating of \\ (m + 8) \text{ kW}, where m is the panel model number. Write an expression in terms of m for the total amount of power produced by 11 solar panels.

7

The representatives of 8 countries are attending a global summit, and each country is able to send (2 r - 3) representatives. Write an expression for the total number of representatives attending the summit.

8

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.

9

Consider the rectangle shown:

Find an expression for the area of the rectangle in expanded form.

10

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

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