Quadratic Expressions Worksheets Page 14
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36number and algebra
2
The spa needs an additional 16 m
of tiles. Write an expression for the total area of
b
tiles needed for both the pool and the spa.
Factorise this expression.
c
Cameron decides to use tiles that are selling at a discount price, but there are only
d
2
280 m
of the tile available. Find the maximum dimensions of the pool he can build
if the width is in whole metres. Assume the spa is to be included in the tiling.
What area of tiles is actually needed to construct the spa and pool?
e
What volume of water can the pool hold?
f
Fabric pieces, comprising yellow squares, white squares and black rectangles are sewn
14
together to make larger squares (patches) as shown in the diagram. These patches are
then sewn together to make a patchwork quilt. A fi nished square quilt, made from 100
2
patches, has an area of 1.44 m
.
y
b
y
Determine the size of each yellow, black and white fabric piece.
a
Show your working.
b
w
b
2
How much (in m
) of each of the coloured fabrics would be
b
needed to construct the quilt? (Ignore seam allowances.)
y
b
y
Sketch a section of the fi nished product.
c
Each factorisation below contains an error. Identify the error in each statement.
15
− 7x + 12 = (x + 3) (x − 4)
2
− x − 12 = (x − 3) (x + 4)
2
x
x
b
a
− x + 2 = (x − 1) (x + 1)
− 4x − 21 = (x − 3) (x − 7)
2
2
x
x
c
d
+ 4x − 21 = (x + 3) (x − 7)
− x − 30 = (x − 5) (x + 6)
2
2
x
x
e
f
2
+ 7x − 8 = (x + 1) (x − 8)
2
− 11x + 30 = (x − 5) (x + 6)
x
x
g
h
PrOblem SOlVIng
Factorise:
16
+ 3 !3x − 6
2
6(3a – 1)
– 13(3a – 1) – 5
a
4
2
3m
– 19m
– 14
b
2
2 sin
(x) – 3 sin(x) + 1
c
Factorise:
17
2
2x
a
doc‐5251
doc‐5251
doc‐5251
3
3
(z + 1)
+ (z – 1)
b
7.4 Factorising expressions with two or
four terms
Factorising expressions with two terms
• If the terms in an expanded expression have a common factor, the highest common
factor is written at the front of the brackets and the remaining factor for each term in the
− 36 = 4(x
− 9).
2
2
expression is written in the brackets. For example, 4x
• A Difference of Two Squares (DOTS) expression in expanded form has two squared
terms separated by a subtraction symbol.
− b
= (a − b) (a + b)
2
2
a
Expanded form
Factorised form
281
Topic 7 • Quadratic expressions
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