Quadratics

Question 1

Expand and simplify: (x - 7)(x + 5)

Answer 1

= x^2 -2x - 35

Question 2

Expand and simplify: (y - 4)(y - 9)

Answer 2

= y^2 - 13y + 36

Question 3

Expand and simplify: -2(4x + 1)(x - 4)

Answer 3

= -2(4x^2 + x - 16x - 4)
= -2(4x^2 - 15x - 4)
= -8x^2 + 30x + 8

Question 4

Expand and simplify: (2p + 1)(2p + 1)

Answer 4

= 4p^2 + 4p + 1

Question 5

Simplify fully: 10 + (x + 2)(x - 5)

Answer 5

= 10 + x^2 + 2x - 5x - 10
= 10 + x^2 - 3x - 10
= x^2 - 3x

Question 6

Simplify fully: (𝑥 + 4)(𝑥 + 3) − (𝑥 + 10)(𝑥 − 3)

Answer 6

= (x^2 + 7x + 12) - (+ x^2 + 10x - 3x - 30)
= 42

Question 7

Expand and simplify: 1 − (4𝑎𝑏 + 𝑐)(𝑎 − 𝑐)

Answer 7

= 1 - 4a^2b - 4abc + ac - c^2
= ac - 4a^b - c^2 - 4abc + 1

Question 8

Expand and simplify: (𝑝 + 3𝑞)(4 − 𝑞) + 7

Answer 8

= 4p + 12q - pq - 3q^2 + 7

Question 9

Factorise the following quadratic: x^2 + 7x + 10

Answer 9

= (x + 2)(x + 5)

Question 10

Factorise the following quadratic: x^2 + x - 6

Answer 10

= (x - 2)(x + 3)

Question 11

Factorise the following quadratic: x^2 - 5x + 6

Answer 11

= (x - 3)(x - 2)

Question 12

Factorise the following quadratic: x^2 - 13x + 30

Answer 12

= (x - 3)(x - 10)

Question 13

Factorise the following quadratic: x^2 - 36

Answer 13

= (x - 6)(x + 6)

Question 14

Factorise the following quadratic: a^2 + 3a - 10

Answer 14

= (a - 2)(a + 5)

Question 15

Solve: x^2 + 11x + 28 = 0

Answer 15

= (x+4)(x+7) = 0
-> x = -4 or -7

Question 16

Solve: x^2 - 12x + 35 = 0

Answer 16

= (x-7)(x-5) = 0
-> x = 7 or 5

Question 17

Simplify: (x^2 + 5x + 4)/(x^2 - x - 2)

Answer 17

= ((x+4)(x+1))/((x+1)(x-2))
-> (x+4)/(x-2)

Question 18

Simplify: (x^2 - 2x - 3)/(9 - x^2)

Answer 18

= ((x-3)(x+1))/((-x+3)(x-3))
-> (x+1)/(-x+3)

Question 19

Solve: 6 = x^2 - 5x

Answer 19

x^2 - 5x - 6 = 0
(x-6)(x+1) = 0
x = 6 or -1

Question 20

Simplify: (x^2 + 4x + 3)/(x^2 + 7x + 12)

Answer 20

= ((x+3)(x+1))/((x+4)(x+3))
->(x+1)/(x+4)

Question 21

Solve: n^2 + 3n - 130 = 0

Answer 21

= (n-10)(n+13) = 0
-> n = 10 or -13

Question 22

Solve: n^2 - 17n - 18 = 0

Answer 22

= (n-18)(n+1) = 0
-> n = 18 or -1

Question 23

Solve: w^2 - 4w - 5 = 0

Answer 23

= (w-5)(w+1) = 0
-> w = 5 or -1

Question 24

Solve: w^2 - 7w + 12 = 0

Answer 24

= (w-4)(w-3)
-> w = 4 or 3

Question 25

Solve: x^2 - 100 = 0

Answer 25

= (x-10)(x+10) -> x = 10 or -10

Question 26

Solve: a^2 - 25a - 264 = 0

Answer 26

(a-33)(a+8) -> a = 33 or -8

Question 27

Solve: -256 + 24x + x^2 = 0

Answer 27

(x-8)(x+32) -> x = 8 or -32

Question 28

Solve: -4x^2 - 312 + 76x = 0

Answer 28

= -4(x^2 + 78 - 19x) = 0 = -4(x-6)(x-13) -> x = 6 or 13

Question 29

Solve: t^2 + 11t - 26 = 0

Answer 29

= (t+13)(t-2) = 0 -> t = -13 or 2

Question 30

Solve: 216 - 6y^2 = 0

Answer 30

= -6(y^2 - 36) = 0 = -6(y-6)(y+6) = 0 -> y = -6 or 6