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Australia
Year 10

1.05 Factorising

Worksheet
Factorise algebraic expressions
1

Find the highest common algebraic factor of the following terms:

a

9 x and 8 x

b

9 x n and 4 a x

c

18 b^{2} n and 7 b^{2} m

d

13 y^{2} a n and 17 m y^{2} b

e

9 b x m and 5 b x a

f

8 m y and 12 a m

g

15 n^{2} m and 8 n m^{2}

h

20 x and 15 x^{2} n

i

16 a b n x and 12 a b m y

j

6abmn and 8bnxy

k

16 a^{2} b x^{3} y^{6} and 12 b^{4} m^{2} n^{6} x

l

12a^7bm^3y^2 and 9ab^5n^2x^3

m

3 b x, 2 n b and 5 b a

n

4 x^{2} a n, 3 b x^{4} m and 12 m a x^{3}

2

Complete the following:

a

y^{2} + 5 y = y \left(⬚ + ⬚\right)

b
2 t^{2} + 2 t = 2 t \left(⬚ + ⬚\right)
c
3 y^{2} + 6 y = ⬚ \left(y + 2\right)
d

- m^{2} + 19 m = ⬚ \left(m - 19\right)

e
- y^{2} - 2 y = ⬚ \left(y + 2\right)
f

8 v - v^{2} = v \left(⬚-⬚\right)

g

11 u - 19 u^{2} = u \left(⬚ - ⬚\right)

h

- 38 x y - 4 y^{2} = ⬚ \left( 19 x + 2 y\right)

3

Factorise:

a
y^{2} + 4 y
b
5 u^{2} - 15 u
c
z^{2} + 8 z^{6}
d
- 18 a + 16
e
- 63 r^{2} + 28
f
3 x - x^{2}
g
k^{2} - 9 k
h
11 k m - m n
i

- 12 s + 10

j
8 h j - 9 g h
k
- 8 w^{2} + 3 w^{2} y
l
16 j k t - 5 k t
m
z^{2} + 6 z^{4}
n
- w^{2} - 6 w
o
5 k^{2} t + 40 k^{3} t^{3}
p
- 45 m n q - 72 m q
q

- 35 m + 49 n

r
49 p^{2} q - 28 p q^{2}
s
- 16 a^{2} - 18 a^{2} b
t
-30w^2-25w^2y
u
44 u v - 8 u^{2} v
v
4mn^2+28m^3n^3
w
-10u^2v+9uv^2
x
12p^2 q^3-28pq^5
4

Factorise:

a
3 t \left(t - 5\right) + 4 \left(t - 5\right)
b
4x \left(y+3\right) +5 \left(y+3\right)
c
5x \left(x - 2\right) -2 \left(x - 2\right)
d
4m \left(m - 7\right) + \left(m-7 \right)
e
7p \left(q +5\right) + 3r\left(q+5 \right)
f
3 \left(x - 1\right)^2 + x\left(x - 1\right)
5

Factorise:

a
20j-15jk-55j^2k
b
3 p^{2} q^{2} + 4 p^{4} q^{4} + 5 p^{6} q^{6}
c
2 y z - 10 x y + 12 x y^{2} z
d
p q r + p^{2} q^{2} r + p^{3} q^{3} r
e
- h f - h j + h g
f
25 m - 15 m n - 10 m^{2} n
6

A student incorrectly used the distributive law and wrote -5x^3-15x=-5x\left(x^2-3\right).

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

7

Find the highest common factor of the terms: 12 p^{2} r^{2} t^{3}, 9 p r t^{3}, and 18 p^{3} r^{3} t^{-2}.

8

12 x^{4} + 18 x^{3} - 24 x^{2} can be factorised into the form 6 x \left( 2 x^{3} + 3 x^{2} - 4 x\right). Has the expression been fully factorised? Explain your answer.

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Outcomes

ACMNA230

Factorise algebraic expressions by taking out a common algebraic factor

ACMNA231

Simplify algebraic products and quotients using index laws

ACMNA232

Apply the four operations to simple algebraic fractions with numerical denominators

ACMNA233

Expand binomial products and factorise monic quadratic expressions using a variety of strategies

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