Expanding Brackets

Expanding brackets means removing the brackets by multiplying each term inside the bracket by the factor outside the bracket.

When expanding a single bracket, multiply each term inside the bracket by the number or variable outside the bracket.

$3 (x + 5)$

Multiply both terms inside the bracket by the 3 on the outside.

$3 \times x + 3 \times 5 = 3 x + 15$

For expanding double brackets, multiply each term in the second bracket by each term in the first.

$(x + 3) (x + 4) = x (x + 4) + 3 (x + 4)$

$x (x + 4) + 3 (x + 4) = x^{2} + 4 x + 3 x + 12$

Then collect the like terms.

$x^{2} + 4 x + 3 x + 12 = x^{2} + 7 x + 12$

Always focus on expanding two brackets at a time. When these brackets are expanded, then multiply each term by each term in the third bracket.

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