AQA GCSE Maths: Algebra: Expressions, Expanding and Factorising

(a) Simplify fully $\frac{x^2 - 9}{2x^2 + 5x - 3}.$2x2+5x−3x2−9​. (3 marks)

(b) Hence, or otherwise, write $\frac{x^2 - 9}{2x^2 + 5x - 3} \times \frac{2x - 1}{x + 3}$2x2+5x−3x2−9​×x+32x−1​ as a single fraction in its simplest form. (2 marks)

(a) Expand and simplify $(2x - 3)(x + 5)$(2x−3)(x+5). (2 marks)

(b) Expand and simplify $(x + 4)^2 - (x - 1)(x - 2)$(x+4)2−(x−1)(x−2). (2 marks)

Make $r$r the subject of the formula $A = \pi r^2 + 2\pi r h.$A=πr2+2πrh. You may leave your answer in terms of a square root.

Hint: treat the formula as a quadratic in $r$r. (4 marks)

Factorise fully $12x^2 y - 18x y^2$12x2y−18xy2. (2 marks)

Then factorise $x^2 - 7x + 12$x2−7x+12. (1 mark)

Simplify $\dfrac{15 a^5 b^3}{3 a^2 b^7}$3a2b715a5b3​. (2 marks)

Simplify $7p - 3q + 2p + 5q$7p−3q+2p+5q. (1 mark)