Expanding binomials and taking out common factors – Year 9 maths test to download as PDF

Expand and simplify where possible.

1. \(5(2x-3)\) (1 mark)
2. \((x+7)(x-3)\) (2 marks)
3. \(3(x+2)-(x-4)\) (1 mark)

Factorise fully.

1. \(12x-18\) (1 mark)
2. \(x^2+9x\) (1 mark)
3. \(15ab+10a^2\) (2 marks)

Expand and simplify.

1. \((x+5)^2\) (2 marks)
2. \((2x+3)(2x-3)\) (1 mark)
3. Factorise \(x^2-64\). (1 mark)

A rectangular lawn is \((x+5)\) metres by \((x+3)\) metres.

1. Show that its area is \(x^2+8x+15\). (2 marks)
2. Find the area when \(x=6\). (1 mark)
3. Turf costs £2.50 per m\(^2\). Find the cost of the turf when \(x=6\). (1 mark)

Sam says: "Think of a number \(n\). Add 3. Multiply by 4. Subtract 12. Divide by your number. The answer is always 4."

1. Write Sam's steps as one algebraic expression. (2 marks)
2. Simplify to show that Sam is right for any \(n\ne0\). (2 marks)