Expanding brackets

Multiply each term inside the bracket by the term outside. Single brackets in Year 7-8; double brackets in Year 9.

Single bracket: a(b + c) = ab + ac. Double bracket: (a+b)(c+d) = ac + ad + bc + bd. The grid (or FOIL: First, Outer, Inner, Last) is a standard method.

Worked examples

3(x + 5) = 3x + 15.

(x + 2)(x + 3) = x² + 5x + 6.

(2x − 1)(x + 4) = 2x² + 7x − 4.

Frequently asked questions

Common error?

Forgetting to multiply EVERY term inside the bracket. 3(x + 5) = 3x + 5 is wrong — the 3 must hit both terms.

Negative outside?

−2(x − 3) = −2x + 6. Both signs flip if the multiplier is negative.