6.12 Factorising
State whether the following are factors of 33 wy:
Find the highest common factor of the following groups of numbers:
2 and 6 x
3 and 15x
6x and 21
10 and 16 u
35 x and 14
4x and 16xy
15 and 5 x
24 m, 12 n and 18 q
27 m, 24 n and 15 q
Complete the factorisation of the following expressions:
2 a + 16 = ⬚ \left(a + 8\right)
5 y - 30 = ⬚ \left(y - 6\right)
24 n + 15 = ⬚ \left( 8 n + 5\right)
16 a - 6 = ⬚ \left( 8 a - 3\right)
6 v + 18 = 6 \left(⬚\right)
9 a - 36 = 9 \left(⬚\right)
24 a + 9 = 3 \left(⬚\right)
6 w - 27 = 3 \left(⬚\right)
4 r + 12 = ⬚ \left(r + 3\right)
5 v - 30 = ⬚ \left(v - 6\right)
18 c - 24 = ⬚ \left( 3 c - 4\right)
2 r + 14 = 2 \left(⬚\right)
5 t - 10 = 5 \left(⬚\right)
54 u + 12 = 6 \left(⬚\right)
Factorise the following expressions:
6 v + 30
6 a - 48
45 t - 40
2 m + 10 n
54 - 60 f g
8 g - 72 h
9 f + 15 g
3 w + 15
2 c - 18
40 c - 35
6 w + 30 y
14 y + 4 w
4 a - 14 b
32 - 36 j k
8 j k t - 18
3 f g - 10 f h
3 r t w - 8 r w
4 r t - 6 r^{2} t
16wy-36w^2y
Complete the following factorisation:
2 w - 10 z + 8 y = 2 \left(⬚ - ⬚ + ⬚\right)
Factorise the following completely:
8 g + 28 h - 20
4 w + 4 z + 4 y
4 u - 12 v + 20 w
10 m - 25 n - 15 p
3 m - 6 n + 12 p
10 g - 35 h + 15
z w - z y - z k
60 r - 25 r t - 35 r^{2} t
12m-32mn-20m^2n
16z-32yz-24y^2z
25 r^2t - 15 r t^2 - 45 r^{2} t^2
Factor out the negative coefficient of the following expressions:
- 4 r - 3 s
- 7 r - 7 s
- 2 - 9 r
- 8x - 5y
Factorise the following expressions:
- 8 b - 16
- 18 a + 16
- 80 v - 30
- 36 - 6 x
- 25 u - 35 v
- 35 m + 49 n
- 8 p q r - 6 p r
- 8 w^{2} + 3 w^{2} y
- 24 j^{2} - 27 j^{2} k
- 8 m^{2} + 9 m n
-10u^2v+9uv^2
-21j^2-36j^2k
- 2 s - 10
- 8 v^{2} + 56
- 12 s + 10
- 28 b - 21
- 63 r^{2} + 28
- 4 m - 32 n
- 49 y - 21 w
Factorise the following completely:
- 18 p - 9 q - 45 r
- 10 r - 25 s + 20 t
- 20 u - 25 v + 45 w
- 8 w - 18 y - 10 z