Foundation and Higher · expanding brackets

Brackets aren't
decoration.

they tell you to multiply.

the one rule —

EXPAND

Each term outside
× each term inside.

example 1 · single bracket

Expand

3(x+2)

× x

× 2

= 3x + 6

1. Multiply every term inside the bracket.

2. 3 × x = 3x.

3. 3 × 2 = 6.

4. Write the two terms side by side.

✓ 3(x + 2) = 3x + 6.

Now two brackets —

example 2 · two brackets

(x+3)(x+5)

x

+3

x

+5

x2

3x

5x

15

x2 + 3x + 5x + 15

x2 + 8x + 15

1. Draw a 2×2 grid, terms on the outside.

2. Multiply across each cell.

3. Add up the four cells.

4. Collect like terms: 3x + 5x = 8x.

✓ x² + 8x + 15.

the one rule

FOIL, grid, arrows —
same rule.
every term × every term.

Forget one pairing —
you lose the whole mark.

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