Year 8 Maths — Algebraic identities

Use (a + b)², (a - b)² and a² - b² to expand brackets and to multiply quickly.

Name: ________________________

1.If a + b = 10 and ab = 21, what is a² + b²?
2.Expand (x + 3)².
- a) x² + 3x + 9
- b) x² + 9
- c) x² + 6x + 6
- d) x² + 6x + 9
3.Factorise a² - b².
- a) (a + b)(a - b)
- b) a(a - b)
- c) (a - b)(a - b)
- d) (a + b)(a + b)
4.Expand (a + b)².
- a) 2a + 2b
- b) a² + b²
- c) a² - 2ab + b²
- d) a² + 2ab + b²
5.Expand (a - b)².
- a) a² - b²
- b) a² + 2ab + b²
- c) a² + b²
- d) a² - 2ab + b²
6.Use a² - b² = (a + b)(a - b) to work out 105 × 95.
7.Expand (x - 5)².
- a) x² - 10x - 25
- b) x² - 25
- c) x² - 10x + 25
- d) x² + 10x + 25
8.Use (100 - 2)² to work out 98².

Answer key — Year 8 Maths — Algebraic identities