Expanding Brackets

≈ 25 min

A number (or letter) in front of a bracket multiplies everything inside. This is the distributive law:

a(b + c) = ab + ac

So each term inside gets multiplied:

3(x + 2) = 3 \times x + 3 \times 2 = 3x + 6

Mind the signs, and remember a letter can multiply a bracket too:

2(3x - 4) = 6x - 8 \qquad x(x + 5) = x^2 + 5x

(Here $x \times x = x^2$ by the multiplying-powers law.)

Worked example. Expand $4(2a + 3)$ .

4 \times 2a + 4 \times 3 = 8a + 12

Expand $4(x + 3)$ .

Which is the correct expansion of $5(2x - 3)$ ?

$10x - 3$

$10x - 15$

$7x - 8$

$10x + 15$

Expand $x(x + 5)$ .

Expand and simplify $2(3a + 4) + 5$ .