Year 8 Maths · KS3 notes

Expanding, factorising and equations

Clear notes with worked examples, then 4 practice questions with answers. Written by Beyond Tutors tutors for the KS3 National Curriculum.

Expanding brackets

Multiply everything inside by the term outside.

$5(x + 3) = 5x + 15$ $-2(x - 4) = -2x + 8$ (negative × negative = positive)

FACTORISING (the reverse)

Take out the highest common factor.

$12x + 18 = 6(2x + 3)$ $x^2 + 7x = x(x + 7)$

EQUATIONS WITH x ON BOTH SIDES

Get the x terms on one side first.

$7x - 4 = 3x + 20$

subtract $3x$ : $4x - 4 = 20$

add 4: $4x = 24$

divide by 4: $x = 6$

Expand first. $4(x - 2) = 2x + 6$ → $4x - 8 = 2x + 6$ → $2x = 14$ → $x = 7$

nth TERM

Difference first, then adjust. 11, 8, 5, 2: difference $-3$ , so $14 - 3n$ .

Check with $n = 1$ : $14 - 3 = 11$ ✓

Try each one, then tap to see the answer and why.