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Expanding Brackets

Multiply every term inside a bracket by the term outside it.

The Distributive Rule

a(b + c) always equals ab + ac. The term outside the bracket multiplies every term inside, one at a time. This is called the distributive law.

Example 1 — easy numbers

Expand 4 (x + 3). 1 Multiply the outside term by the first term inside: 4 \times x = 4 x 2 Multiply the outside term by the second term inside: 4 \times 3 = 12 3 Write the two results with a plus between them: 4 x + 12 Answer: 4 x + 12

Example 2 — a negative outside term

Expand - 2 (x - 5). 1 Multiply: - 2 \times x = - 2 x 2 Multiply: - 2 \times (- 5) = 10 (two negatives make a positive) 3 Combine: - 2 x + 10 Answer: - 2 x + 10

Example 3 — expanding then simplifying

Expand and simplify 3 (x + 4) + 2 x . 1 Expand the bracket: 3 (x + 4) = 3 x + 12 2 Rewrite the full expression: 3 x + 12 + 2 x 3 Collect like terms: 3 x + 2 x = 5 x 4 Final answer: 5 x + 12 Answer: 5 x + 12

Example 4 — two brackets

Expand and simplify 2 (x + 3) + 3 (x - 1). 1 Expand the first bracket: 2 (x + 3) = 2 x + 6 2 Expand the second bracket: 3 (x - 1) = 3 x - 3 3 Combine: 2 x + 6 + 3 x - 3 4 Collect like terms: 2 x + 3 x = 5 x, and 6 - 3 = 3 5 Final answer: 5 x + 3 Answer: 5 x + 3

Practice

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What does 5 (x - 2) expand to?

Expand and simplify 3 (x + 2) + 2 (x + 1), then enter the coefficient of x .

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