Expanding Single Brackets

In a Nutshell

Expanding means multiplying every term inside the bracket by the number outside — no term left behind.

When you see a number or letter outside a bracket, it multiplies every term inside the bracket. This is called expanding (or removing) the bracket.

3(x+4)=3×x+3×4=3x+123(x + 4) = 3 \times x + 3 \times 4 = 3x + 12

Think of it as the distributive law: the multiplier is distributed to each term in the bracket. It works just the same when there is a subtraction inside:

5(2y−3)=5×2y−5×3=10y−155(2y - 3) = 5 \times 2y - 5 \times 3 = 10y - 15

If a negative number is outside the bracket, remember the sign rules: −(x+2)=−x−2-(x + 2) = -x - 2.

See it: distribution is area

Expanding brackets as area of rectangles A rectangle is split into two parts to show that multiplying a bracket is the same as finding areas of two smaller rectangles and adding them.
Try:

The rectangle above has width equal to the multiplier and length split into two parts. Press Expand to watch it split into two sub-rectangles — their areas give you the expanded terms. Try different expressions to see the pattern.

Watch it work

Question: Expand 4(3x+2)4(3x + 2).

Question 2: Expand −2(3a−5)-2(3a - 5).

Have a go

Q1. Expand 2(x+5)2(x + 5).

Q2. Expand 6(3y−1)6(3y - 1).

Q3. Expand x(x+7)x(x + 7).

Q4. Expand and simplify 3(x+4)+2(x−1)3(x + 4) + 2(x - 1).