Expanding linear brackets

Topic summary

Expanding means to multiply out the brackets. Multiply each term inside the bracket by the term on the outside of the bracket.

For simple brackets:

\[ a(b + c) = a \times b + a \times c \]

How to expand

\[3(x+4)\]

Multiply each term by the 3 on the outside of the brackets.

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

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

Harder expansions

\[2x(3x+10)\]

Multiply each term by the 2x on the outside of the brackets.

\[ 2x(3x+10) = 2x \times 3x + 2x \times 10 \]

\[ 2x(3x+10) = 6x^2 + 20x\]