Quadratic Expressions Worksheets Page 23
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36Q
R
NUMBER AND ALGEBRA
Q
R
Write the expression as a
3
2
9
81
=
x −
−
+ 1
Q
R
Q
R
!77
difference of two squares by:
2
4
#
• simplifying the numerical
2
9
77
Q
R
Q
R
=
x −
−
!77
terms
= 1 x −
2 1 x −
2
2
4
• writing the numerical term
2
2
9
!77
!77
=
x −
−
as a square.
2
2
where a = a x +
b and
2
2
77
77
=
=
4
4
2
Use the pattern for DOTS:
4
9
9
+
−
!77
− b
= (a − b) (a + b),
2
2
2
2
2
2
a
9
2
b =
.
2
• Remember that you can expand the brackets to check your answer.
2
• If the coef cient of x
1, factorise the expression before completing the square.
Exercise 7.5 Factorising by completing the square
INDIVIDUAL PATHWAYS
REFLECTION
PRACTISE
CONSOLIDATE
MASTER
Why is this method called
Questions:
Questions:
Questions:
completing the square?
1a–d, 2a–d, 3a–d, 4a–d,
1e–i, 2e–h, 3e–h, 4e–h, 5–8, 10
1g–i, 2g–i, 3g–i, 4g–i, 5–11
5–7, 9
Individual pathway interactivity
int-4599
FLUENCY
Complete the square for each of the following expressions.
1
WE10
+ 10x
+ 6x
− 4x
2
2
2
x
x
x
a
b
c
2
+ 16x
2
− 20x
2
+ 8x
x
x
x
d
e
f
− 14x
+ 50x
+ 7x
2
2
2
x
x
x
g
h
i
2
− x
x
j
Factorise each of the following by rst completing the square.
2
WE11a
− 4x − 7
+ 2x − 2
− 10x + 12
2
2
2
x
x
x
a
b
c
+ 6x − 10
+ 16x − 1
− 14x + 43
2
2
2
x
x
x
d
e
f
+ 8x + 9
− 4x − 13
− 12x + 25
2
2
2
x
x
x
g
h
i
Factorise each of the following by rst completing the square.
3
WE11b
− x − 1
− 3x − 3
+ x − 5
2
2
2
x
x
x
a
b
c
+ 3x − 1
+ 5x + 2
+ 5x − 2
2
2
2
x
x
x
d
e
f
− 7x − 1
− 9x + 13
− x − 3
2
2
2
x
x
x
g
h
i
Factorise each of the following by rst looking for a common factor and then
4
completing the square.
+ 4x − 4
− 8x − 20
+ 30x + 5
2
2
2
2x
4x
5x
a
b
c
− 12x − 39
− 30x + 10
+ 24x − 6
2
2
2
3x
5x
6x
d
e
f
+ 30x + 39
− 8x − 14
+ 36x − 30
2
2
2
3x
2x
6x
g
h
i
Maths Quest 10 + 10A
290
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