1 Algebra
Australia
Year 10
1.07 Factorising binomial products
Worksheet
1
Factorise:
a
5 \left(a + b\right) + v \left(a + b\right)
b
x \left(y - z\right) - w \left(y - z\right)
c
5 y \left( 4 w + 3 x\right) - z \left( 4 w + 3 x\right)
d
2 y \left( 2 x^{2} + 3 z\right) - \left( 2 x^{2} + 3 z\right)
e
3 f \left(g + h\right) + \left(g + h\right)^{2}
f
8 y \left(y - 4\right) + 3 \left(4 - y\right)
g
\left( 2 c - d\right) \left(c + 5 d\right) - 3 \left(d - 2 c\right)
h
3x^2\left(x+4y\right)-5y\left(x+4y\right)
2
Factorise:
a
8 x + x z - 16 y - 2 y z
b
24 + 3 y + 8 x + x y
c
7 x y + w x + 7 y z + w z
d
x^{2} + 2 x + 5 x + 10
e
x^{2} - 3 x + 8 x - 24
f
2 m p + 6 + 3 p + 4 m
g
a^{3} + 8 a^{2} + a + 8
h
3 p q^{2} - 11 y p q + 3 r s q - 11 y r s
i
4 x + 24 y z + 32 x y + 3 z
j
2x+18yz+12xy+3z
3
Factorise:
a
a^2+14a+49
b
g^2-12g+36
c
x^2+24x+144
d
y^2-18y+81
e
z^2-4z+4
f
4w^2+20w+25
g
64c^2+112c+49
h
9n^2-24n+16
4
Factorise:
a
q^{2} + 2 q t + t^{2}
b
u^{2} - 2 u q + q^{2}
c
b^2-2br+r^2
d
x^2+6x+9
e
c^2-4c+4
f
64+16e+e^2
g
49-14p+p^2
h
16w^2-40w+25
i
64r^2+48r+9
j
\dfrac{1}{4}-3d+9d^2
5
A square has an area of \left( t^2+14t+49 \right) \text{ cm}^2.
a
Find the side length of the square.
b
Find the value of t if the perimeter of the square is 36\text{ cm}.
6
One linear factor of x^{2} - 16 is x- 4. Find the other factor.
7
What can we multiply z + 7 by to give the difference of two squares?
8
Factorise:
a
x^{2} - y^{2}
b
n^{2} - 25
c
v^{2} - 1
d
121 - v^{2}
e
x^{2} - \dfrac{1}{4}
f
x^{2} - \dfrac{25}{121}
g
16 - 9 y^{2}
h
x^{2} y^{2} - 49
i
25 m^{2} - 49
j
81 x^{2} - 16 y^{2}
k
7 x^{2} - 63
l
45 t^{2} - 20
9
Using the difference of two squares, evaluate the following:
a
65^{2} - 63^{2}
b
99^2-97^2
c
45^2-42^2
d
58^2-52^2
10
Find the value of the following by rewriting in the form \left(x + y\right) \left(x - y\right):
a
504\times 49
b
304 \times 296
11
Consider the shaded area shown:
a
Find the area of the shaded region.
b
State whether the following rectangles have the same area as the shaded region from part a.
i
ii
iii
12
Factorise:
a
3x^2 y-6y^4+9x^2 y^3
b
16x^2 y^2+24xyz+9z^2
c
121c^2-49d^2
d
3x^2y+x^2 z+3y^2+yz
e
a^2+2ab+b^2-c^2
f
8a^2b^4+12bc^2
g
\left(b+4\right)^2-\left(3-b\right)^2
h
14h^3 p^2 r+21h^5 p^2+49hp^4
i
8w^2-32wt^2+3wt-12t^3
j
16q^4+24q^2r+9r^2
k
48df^2-3dh^2
l
128t^3-18s^4t
m
18j^2+60jk+50k^2
n
x^2 y+7x^2-y-7
13
Factorise x^4-1.
14
Factorise:
a
x^4-8x^2+16
b
a^4-18a^2+81
c
16y^4-72y^2+81
d
25-\dfrac{20}{z}+\dfrac{4}{z^2}
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