Quadratic Expressions Worksheets Page 17
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36NUMBER AND ALGEBRA
Factorise each of the following by taking out a common binomial factor.
2
3x(x − 2) + 2(x − 2)
5(x + 3) − 2x(x + 3)
a
b
(x − 1)
2
+ 6(x − 1)
(x + 1)
2
− 2(x + 1)
c
d
(x + 4) (x − 4) + 2(x + 4)
7(x − 3) − (x + 3) (x − 3)
e
f
Factorise each of the following.
3
WE7
doc 5246
doc 5246
doc 5246
2
− 1
2
− 9
2
− 25
x
x
x
a
b
c
− 100
− k
− 9y
2
2
2
2
2
x
y
4x
d
e
f
− 49
− 36q
1 − 100d
2
2
2
2
16a
25p
g
h
i
doc 5247
doc 5247
doc 5247
Factorise each of the following.
4
WE7
− 4
− 80
− 9a
2
2
2
4x
5x
ax
a
b
c
− 8d
− 1600
− 147a
2
2
2
2
2b
100x
3ax
d
e
f
− 256p
− 16
108 − 3x
2
2
2
4px
36x
g
h
i
a
b a
b
If the factorised expression is (x + 7) (x − 7), then the expanded expression
5
MC
a
( !3)
( !3)
must have been:
− 7
+ 7
− 49
+ 49
− 14x + 49
2
2
2
2
2
x
x
x
x
( !5)
x
( !5)
A
B
C
D
E
3
3
x
x
If the factorised expression is
−
+
, then the original expression must have
b
4
5
4
5
been:
2
2
2
2
2
x
3
x
9
2
x
9
2
x
x
−
−
−
−
−
A
B
D
C
E
4
5
16
25
4
25
4
16
2
2
− 9y
2
2
The factorised form of 64x
is:
c
(64x + 9y) (64x − 9y)
(8x + 3y) (8x − 3y)
A
B
(8x − 3y) (8x − 3y)
(8x + 3y) (8x + 3y)
C
D
(16x + 3y) (16x − 3y)
E
Which of the following expressions would be factorised by grouping ‘two
6
MC
and two’?
− a
+ 12a − 36
− 7x − 10
2
2
2
x
x
A
B
(s − 5)
− 25(s + 3)
− 6x − xy + 3y
2
2
2
2x
D
C
(r + 5) − (r + 3) (r + 5)
E
Factorise each of the following over the set of real numbers.
7
WE7
− 11
− 7
− 15
2
2
2
x
x
x
a
b
c
− 13
− 19
− 66
2
2
2
4x
9x
3x
d
e
f
− 15
− 4
− 36
2
2
2
5x
2x
12x
g
h
i
Factorise each of the following expressions.
8
(x − 1)
2
− 4
(x + 1)
2
− 25
a
b
(x − 2)
− 9
(x + 3)
− 16
2
2
c
d
49 − (x + 1)
36 − (x − 4)
2
2
e
f
(x − 1)
− (x − 5)
4(x + 2)
− 9(x − 1)
2
2
2
2
g
h
25(x − 2)
− 16(x + 3)
2
2
i
Factorise each of the following.
9
WE8a
x − 2y + ax − 2ay
2x + ax + 2y + ay
a
b
ax − ay + bx − by
4x + 4y + xz + yz
c
d
ef − 2e + 3f − 6
mn − 7m + n − 7
e
f
Maths Quest 10 + 10A
284
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