Expanding brackets and simplifying practice

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

Multiply every pair, then collect.

Like terms: same letters, same powers. Add their numbers only.
One bracket: the outside term multiplies every inside term, sign included.
Two brackets: four products, then collect the middle two.
Squares: write \((a + b)^{2}\) as \((a + b)(a + b)\).
Three brackets (Extended): expand two, simplify, then multiply by the third.

Recall

[2 marks]

Simplify (a) \(7p + 3q - 2p - 8q\) (b) \(3x^{2} + 4x - x^{2} - 6x\).

(a) \(5p - 5q\) ✓
(b) \(2x^{2} - 2x\) ✓

Recall

[2 marks]

Expand (a) \(5y(3y - 2)\) (b) \(-2a(4a + 3b)\).

(a) \(15y^{2} - 10y\) ✓
(b) \(-8a^{2} - 6ab\) ✓

Calculation

[2 marks]

Expand and simplify \(4(3x + 2) - 3(2x - 5)\).

\(12x + 8 - 6x + 15\) ✓
\(= 6x + 23\) ✓

Calculation

[4 marks]

Expand and simplify (a) \((x + 7)(x - 3)\) (b) \((4x - 1)^{2}\).

(a) \(x^{2} - 3x + 7x - 21 = x^{2} + 4x - 21\) ✓
(b) \((4x - 1)(4x - 1) = 16x^{2} - 4x - 4x + 1 = 16x^{2} - 8x + 1\) ✓

Calculation

[3 marks]

(Extended) Expand and simplify \((x + 1)(x - 3)(2x + 5)\).

\((x + 1)(x - 3) = x^{2} - 2x - 3\) ✓
\((x^{2} - 2x - 3)(2x + 5) = 2x^{3} + 5x^{2} - 4x^{2} - 10x - 6x - 15\) ✓
\(= 2x^{3} + x^{2} - 16x - 15\) ✓

Analysis

[4 marks]

A rectangular card measures \((2x + 3)\) cm by \((x + 4)\) cm. A square of side \(x\) cm is cut out of it.

(a) Show that the area of card left is \((x^{2} + 11x + 12)\) cm².

(b) Find the area left when \(x = 5\).

(a) Rectangle: \((2x + 3)(x + 4) = 2x^{2} + 8x + 3x + 12 = 2x^{2} + 11x + 12\) ✓
Subtract the square: \(2x^{2} + 11x + 12 - x^{2} = x^{2} + 11x + 12\) ✓
(b) \(25 + 55 + 12 = 92\) cm² ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.