Expanding Brackets

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

Expanding Single Brackets

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.

\[3 \times x + 3 \times 5 = 3x + 15\]

Expanding Double Brackets

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

\[(x + 3)(x + 4) = x(x + 4) + 3(x + 4)\]

\[x(x + 4) + 3(x + 4) = x^2 + 4x + 3x + 12\]

Then collect the like terms.

\[x^2 + 4x + 3x + 12 = x^2 + 7x + 12\]

Expanding Triple Brackets

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.