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2 Algebra
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Level 9

2.02 The distributive law

Lesson
Worksheet
Practice
Worksheet
Distributive law
1

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

Explain how to correct the error, and write the correct answer.

2

Expand:

a
5 \left(s - 4\right)
b
8 \left(c + 4\right)
c
a \left(b + 7\right)
d
- m \left( 11 n + 19 p\right)
e
6 s \left( 9 t + 8\right)
f
4 \left(m^{2} + 10\right)
g
m \left(m + 7\right)
h
y \left(1 + y\right)
i
m \left(m - 3\right)
j
- w \left(w + 1\right)
k
y \left( 4 y - 10\right)
l
m \left(8 - m\right)
m
5 t \left(t + 14\right)
n
- 4 t \left( 4 t + 3\right)
o
7 s^{3} \left( 8 t^{5} - 9\right)
p
2 b \left( 2 b + 16\right)
q
- 5 a \left( 3 a - 4\right)
r
\dfrac{y}{5} \left( 10 y + 60\right)
s
7 y \left(y^{2} + 4\right)
t
6 w y \left(y + w\right)
u
\left( 5 y - 6\right) \left( - 3 y^{2} \right)
v
4 u^{7} \left( 4 u^{7} + 2 u^{6}\right)
w
3 u^{4} \left( 8 u + 10 u^{3}\right)
x
-3x^2\left(5x-2x^4\right)
3

Expand:

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

Complete the following:

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
5

Expand and simplify:

a
- 21 n \left(\dfrac{n}{3} + 7\right)
b
- 25 n \left(\dfrac{n}{5} + 2\right)
c
8 \left(y + 6\right) + 3 \left(y + 9\right)
d
5 \left( 9 x - 6 y\right) - 3 \left( 8 y + 2 x\right)
e
2 \left( 4 \left(x - 3\right) + 5\right)
f
3\left(2\left(x-4\right)+5\right)
g
3 c \left( 9 c^{2} + 2 c + 7\right)
h
x \left(x + 6\right) + 8 \left(x + 7\right)
i
4 y^{2} - 9 y + 6 y \left(y - 8\right)
j
6 u \left( 5 u + 8 v\right) - 7 u \left( 4 v + 2 u\right)
k
4c\left(8c^2-3c-5\right)
l
x\left(x+4\right)+2\left(x+5\right)
m
8y^2-7y+9y\left(y-5\right)
n
9x\left(6x+8y\right)-7x\left(2y+4x\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.

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Outcomes

VCMNA306

Apply the distributive law to the expansion of algebraic expressions, including binomials, and collect like terms where appropriate.

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