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

Factorise 121 - y²

Answer 7

(11-y)(11+y)

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

Question 8

Factorise 4x² - 9y²

Answer 8

(2x+3y)(2x-3y)

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

Question 9

Factorise 64a² - 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