Expanding and Factorising Quadratics

Question 1

Expand and simplify: (x+4)(x+5)

Answer 1

x2 + 9x + 20

Question 2

Expand and simplify: (x+4)(x-5)

Answer 2

x2 - x - 20

Question 3

Expand and simplify: (x-12)(x-5)

Answer 3

x2 - 17x + 60

Question 4

Factorise x2 - 9

Answer 4

(x-3)(x+3)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 5

Factorise x2 - 1

Answer 5

(x-1)(x+1)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 6

Factorise x2 - y2

Answer 6

(x-y)(x+y)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 7

Factorise121 - y2

Answer 7

(11-y)(11+y)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 8

Factorise4x2 - 9y2

Answer 8

(2x+3y)(2x-3y)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 9

Factorise64a2 - 49y2

Answer 9

(8a+7y)(8a-7y)use the difference of two squares rule x2 - a2 = (x-a)(x+a)

Question 10

Factorise x2 + 8x- 33

Answer 10

(x+11)(x-3)

Question 11

Factorise x2 - 8x- 33

Answer 11

(x-11)(x+3)

Question 12

Complete the square for x2 + 6x - 2

Answer 12

(x + 3)2 - 11

Question 13

Complete the square for x2 - 8x + 3

Answer 13

(x - 4)2- 13