Expanding Brackets & Factorisation - Past Paper Questions - ANSWERS
1)
3(2x – 4) – 4(3x + 1)
6x – 12 – 12x – 4
–6x – 16
2)
(2a – b)(3a + 2b)
6a2 + 2ab – 3ab – 2b2
6a2 – ab – 2b2
3)
(2x – 5)(3x + 1)
6x2 + 2x – 15x – 5
6x2 – 13x – 5
4)
(2x – 1)(x + 4)
2x2 + 8x – x – 4
2x2 + 7x – 4
5)
(x + 4)(3x – 1)
3x2 – x + 12x – 4
3x2 + 11x – 4
6)
(2x + 6)(5x – 3) + 9x
10x2 – 6x + 30x – 18 + 9x
10x2 + 33x – 18
7)
(3x + 2)(x – 5) + 8x
3x2 – 15x + 2x – 10 + 8x
3x2 – 5x – 10
8)
(x + 2)(x – 5) – 9x
x2 – 5x + 2x – 10 – 9x
x2 – 12x – 10
9)
(4x + 2)(x – 5) + 3x
4x2 – 20x + 2x – 10 + 3x
4x2 – 15x – 10
10)
5x + (x – 4)(3x + 1)
5x + 3x2 + x – 12x – 4
3x2 – 6x – 4
11)
(2x + 3)2 – 3(x2 – 6)
12)
4x2 + 6x + 6x + 9 – 3x2 + 18
x2 + 12x + 27
(x – 3)(x2 + 4x – 1)
x3 + 4x2 – x – 3x2 – 12x + 3
x3 + x2 – 13x + 3
13)
(x – 4)(x2 + x – 2)
x3 + x2 – 2x – 4x2 – 4x + 8
x3 – 3x2 – 6x + 8
14)
(3x – 5)(x2 + 2x – 6)
15)
3
2
2
3x + 6x – 18x – 5x – 10x + 30
3x3 + x2 – 28x + 30
(3x + 2)(x2 + 5x – 1)
3x3 +15x2 –3x +2x2 +10x – 2
3x3 + 17x2 + 7x – 2
16)
(x + 5)(2x2 – 3x – 1)
17)
2x3 – 3x2 – x + 10x2 – 15x – 5
2x3 + 7x2 – 16x – 5
(x + 3)(x2 + 4x – 12)
18)
x3 + 4x2 – 12x + 3x2 + 12x – 36
x3 + 7x2 – 36
(2y – 3)(y2 + 4y – 1)
2y3 + 8y2 – 2y – 3y2 – 12y + 3
2y3 + 5y2 – 14y + 3
19)
(2x – 5)(x2 + 3x – 7)
20)
2x3 + 6x2 – 14x - 5x2 – 15x + 35
2x3 + x2 – 29x + 35
(3x – 2)(2x2 + x + 5)
21)
6x3 + 3x2 + 15x – 4x2 – 2x – 10
6x3 – x2 +13x – 10
(3x + 1)(x2 – 5x + 4)
3x3 –15x2 +12x + x2 –5x + 4
3x3 – 14x2 + 7x + 4
22)
x(x – 1)2
x(x – 1)(x – 1)
x(x2 – x – x + 1)
x(x2 – 2x + 1)
x3 – 2x2 + x
23)
6ab – 7bc
b(6a – 7c)
24)
3y2 – 6y
3y(y – 2)
25)
4p2 – 49
(2p + 7)(2p – 7)
26)
2x2 – 18
2(x2 – 9)
2(x + 3)(x – 3)
27)
5x2 – 45
5(x2 – 9)
5(x + 3)(x – 3)
28)
p2 – 4q2
(p + 2q)(p – 2q)
29)
x2 – 4y 2
(x + 2y)(x – 2y)
30)
4x2 – y2
(2x + y)(2x – y)
31)
x2 – 4x – 21
(x – 7)(x + 3)
32)
y2 + y – 6
(y + 3)(y – 2)
33)
x2 – 5x – 24
(x – 8)(x + 3)
34)
x2 + x – 6
(x + 3)(x – 2)
35)
7 + 6x – x2
(7 – x)(1 + x)
36)
3x2 + 9x – 12
3(x2 + 3x – 4)
3(x + 4)(x – 1)
37)
2p2 – 5p – 12
(2p + 3)(p – 4)
38)
3x2 – 7x + 2
(3x – 1)(x – 2)
39)
a)
b)
x2 – y2
(x + y)(x – y)
9·32 – 0·72
(9·3 + 0·7)(9·3 – 0·7)
(10)(8·6)
86
40)
a)
b)
a2 + 2ab + b2
(a + b)(a + b)
942 + 2 × 94 × 6 + 62
(94 + 6)(94 + 6)
(100)(100)
10 000