Factorise completely:
(a) xy2−x

(b) x2+4x−12

Factorise fully: 3x2y−6xy

Factorise fully: 4x2−y2

Factorise completely:
(a) 2mn+n2

(b) xy2−9x

Factorise: a2+a−2ab−2b

Factorise completely: 2xy+6xz

c=x(a+b)
(a) Evaluate c when x=3, a=5 and b=−7

(b) Make b the subject of the formula.

(a) Factorise:
(i) a2b+6b2a

(ii) b2−36

(a) Simplify: 3x(2x+3)−(9x+5)
(b) Express as a single fraction in its simplest form:
2c−13−c−22
(c) Factorise completely:
(i) x2+6x−16
(ii) 2x2+xy−x−2y−6

(a) Factorise completely: $6xa-3y-9x+2ay$

(b) $1+\frac{2x-5}{3}-\frac{x+3}{2}$

(c) Express as a single fraction in its simplest form.

(a) Make p the subject of the formula: $2p+q=kp+4$

(b) Express as a single fraction in its simplest form.

The diagram shows a rectangle of length (x + 9) and width x cm.

(i) Write an expression in terms of x for the perimeter of the rectangle. Give your answer in its simplest form.

(ii) The length and the width of the rectangle are in the ratio 3:1. Calculate the width of the rectangle.

Evaluate $\frac{\sqrt[3]{{7.67}^2+12}}{6.8}$.

(a) $p=mv-mu$

(b) Express as a single fraction: $\frac{2x-1}{3}-\frac{3x+2}{5}$

(c) Remove the brackets and simplify: $2(3x-4y)$ − $3(x+2y)$

(a) Simplify: $3(x+2)$ − $(2x+7)$

(b) Factorise completely: $ac-ad+bc-bd$