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AustraliaNSW
Stage 5.1-3

2.03 Binomial expansion

Worksheet
Binomial expansion
1

Expand and simplify:

a
\left(x + 6\right) \left(x - 12\right)
b
\left(x + 2\right) \left(x + 6\right)
c
\left(v + 11\right) \left(v + 10\right)
d
\left(x - 4\right) \left(x - 7\right)
e
\left(m - 5\right) \left(m + 6\right)
f
\left( 10 m + 9\right) \left(m - 7\right)
g
\left( 3 w + 5\right) \left( 7 w + 6\right)
h
\left( 3 y - 3\right) \left( 10 y + 9\right)
i
\left( 7 y + 9\right) \left( - 4 y - 4\right)
j
3 \left(y + 3\right) \left(y + 5\right)
k
8 \left(x - 2\right) \left(x - 6\right)
l
- \left(x + 5\right) \left(x + 6\right)
m
- 4 \left(y + 1\right) \left(y + 9\right)
n
- 9 \left(y - 7\right) \left(y + 6\right)
o
3 \left( - 4 x + 3\right) \left( 4 x - 3\right)
p
4 \left( 6 x - 2\right) \left(x + 2\right)
2

Complete the following:

a
\left(t + 8\right) ⬚ = t^{2} + 10t + 16
b
\left(t + 6\right) ⬚ = t^{2} + 17 t + 66
c
\left(t - 2\right) ⬚ = t^{2} - 7 t + 10
d
\left(t - 2\right) ⬚ = t^{2} + 4 t - 12
e

\left(t + 2\right) \left(t + 9\right)=t \left(t + 9\right)+ ⬚ \left(⬚\right)

f

\left(v - 2\right) \left(v - 3\right)=v \left(v - 3\right)-⬚ \left(⬚\right)

g

\left(t - 2\right) \left(t + 8\right) = t \left(t + 8\right) - ⬚

h
\left(t - 5\right) ⬚ = t^{2} + 7 t - 60
3

State whether the following expressions are equivalent to \left(y - 5\right) \left(y - 8\right):

a
5 \left(y - 8\right) - \left(y - 5\right)
b
y \left(y - 5\right) + y - 8
c
y \left(y - 5\right) + 8 \left(y - 8\right)
d
y \left(y - 8\right) - 5 \left(y - 8\right)
4

What expression when multiplied by n + 6 gives n^{2} + 14 n + 48?

5

Expand:

a
(2x+3)(x+5y-4z)
b
\left(t+3\right)\left(2t-1\right)\left(3t+5\right)
6

A student wrote \left(a+b\right)^2=a^2+b^2. Explain why they are incorrect and write the correct answer.

Applications
7

If the smallest of three consecutive integers is n, find the product of the three integers. Write your answer in expanded form.

8

Consider the rectangular prism shown with its dimensions labelled. Write an expression for the volume, and then expand and fully simplify the result.

9

The area of the figure below is \left(y + 3\right) \left(y + 6\right). We want to find another expression for this area by finding the sum of the areas of the four smaller rectangles.

a

State the area of rectangle A.

b

State the area of rectangle B.

c

State the area of rectangle C.

d

State the area of rectangle D.

e

Hence, write an equivalent expression for the area of the figure.

10

Find the area of a reactangle which has a length of \left(x+4\right)\text{ cm} and a width of \left(x+3\right)\text{ cm}.

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Outcomes

MA5.2-6NA

simplifies algebraic fractions, and expands and factorises quadratic expressions

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