Factorise the following expressions:
10 x + 50
7 v - v^{2}
z^{2} + 4 z^{4}
Factorise the following expressions:
6 y \left(y - 7\right) + 5 \left(7 - y\right)
2 f \left(g + h\right) + \left(g + h\right)^{2}
\left(y + 4\right) \left(y + 7\right) + x \left(y + 7\right)
2 \left(x + 9\right) \left(x - 5\right)^{3} + 3 \left(x + 9\right)^{2} \left(x - 5\right)^{2}
Complete the factorisation process below:
\begin{aligned}mnp+m+x+xnp&=⬚(np+1)+x(1+ ⬚)\\&= m(np+1)+x(⬚+1)\\&= (np+1)(⬚+⬚)\end{aligned}
Factorise the following expressions:
3 x + x z - 39 y - 13 y z
6 y - y w + w^{2} - 6 w
x^{2} - y^{2} - x - y
If p - 10 q + p r - 10 q r = 72 and 1 + r = 12, find the value of p - 10 q by first factorising the expression p - 10 q + p r - 10 q r.
Factorise the following expressions:
k^{2} - 81
16 m^{2} - 81
x^{2} - \dfrac{4}{49}
\left(x + 13\right)^{2} - y^{2}
\left( 5 x + 4\right)^{2} - \left( 3 x - 1\right)^{2}
u^{2} m^{2} - 121
5 x^{2} - 320
x^{4} - 1
Factorise the following:
x^{2} + 12 x + 36
36 - 12 u + u^{2}
s^{2} - 2 s t + t^{2}
x^{2} + 3 x + \dfrac{9}{4}
81 x^{2} + 36 x + 4
81 t^{2} + 72 t + 16
p^{3} + 8 p^{2} q + 16 p q^{2}
Simplify the following expression:
\sqrt{ x^{2} y^{2} + 18 x y^{2} + 81 y^{2}}
To factorise the quadratic x^{2} + 11 x + 24, we need to find two numbers.
What should the product of the two numbers equal?
What should the sum of the two numbers equal?
Complete the following statement:
\left(m + 8\right)(⬚)=m^{2} + 18 m + 80
Find the values of m and n in the following equation:
y^{2} + m y + 60 = \left(y + 10\right) \left(y + n\right)
Factorise the following:
x^{2} + 16 x + 60
t^{2} - 14 t + 48
x^{2} - 2 x - 8
t^{2} + 6 t - 16
x^{4} - 10 x^{3} + 24 x^{2}
What is the largest possible integer value of k that will allow m^{2} + k m + 24 to be factorised?
Find an expression for the shaded area in the figure in terms of x. Write your answer in factorised form.
Factorise the following:
4 x^{2} + 40 x + 100
- 3 x^{2} + 12 x - 12.
Find the value of k that will make 16 x^{2} - 24 x + k a perfect square trinomial.
A cube has a surface area of \left(6 x^{2} + 36 x + 54\right) square units, where x > 0.
Factorise 6 x^{2} + 36 x + 54 completely.
Hence, find an expression for the length of a side of the cube.
Quadratic trinomials can be factorised using the identity:
a x^{2} + b x + c = \dfrac{\left( a x + m\right) \left( a x + n\right)}{a}where m + n = b and m n = a c.
Find the values m and n for the quadratic 4 x^{2} - 14 x + 12.
Consider the figure below:
Write an expression in expanded form for the area of the shaded region.
Write the expression for the area as a factorised quadratic.
Factorise the following:
8 h j - 9 g h
x \left(y - z\right) - w \left(y - z\right)
5 y \left( 4 w + 3 x\right) - z \left( 4 w + 3 x\right)
8 x + x z - 16 y - 2 y z
7 x y + w x + 7 y z + w z
v^{2} - 49
121 - v^{2}
x^{2} - \dfrac{1}{4}
x^{2} + 16 x + 64
x^{2} - 20 x + 100
64 + 16 x + x^{2}
x^{2} + 11 x + 24
x^{2} + 17 x + 72
3 x^{2} - 21 x - 54
- 5 x^{2} + 10 x + 40
16 m^{2} - 81
5 k^{2} t + 40 k^{3} t^{3}
3 p q^{2} - 11 y p q + 3 r s q - 11 y r s
81 t^{2} + 72 t + 16
- 45 m n q - 72 m q
3 x^{2} + 24 x + 48
z^{2} + 4 z^{4}
7 x^{2} - 75 x + 50
x^{2} - 17 x + 60
2 y \left( 2 x^{2} + 3 z\right) - \left( 2 x^{2} + 3 z\right)
8 y \left(y - 4\right) + 3 \left(4 - y\right)
Factorise the following:
- h f - h j + h g
2 y z - 10 x y + 12 x y^{2} z
x^{2} + 2 x + 5 x + 10
x^{2} - 19 x + 84
x^{2} - x - 30
9 x^{2} - 19 x + 10
6 x^{2} + 13 x + 6
3 f \left(g + h\right) + \left(g + h\right)^{2}
\left( 2 c - d\right) \left(c + 5 d\right) - 3 \left(d - 2 c\right)
a^{3} + 8 a^{2} + a + 8
4 x + 24 y z + 32 x y + 3 z
44 u v - 8 u^{2} v
- h f - h j + h g
x^{2} + x - 20
x^{2} - 3 x - 54
- 10 x^{2} - 7 x + 12
8 - 14 p - 49 p^{2}
2 y z - 10 x y + 12 x y^{2} z
3 p^{2} q^{2} + 4 p^{4} q^{4} + 5 p^{6} q^{6}
x^{2} - \dfrac{25}{121}
25 m^{2} - 49
- 4 x^{2} + 40 x - 100
- 8 - 6 x - x^{2}
- 12 + 7 x - x^{2}
56 - 41 b - 6 b^{2}