Expanding quadratic brackets

Topic summary

We expand quadratic brackets the same way we expand linear brackets, but this time there are two terms outside the bracket.

For simple brackets:

\[ (a + b)(c + d) = ac + ad + bc + bd \]

How to expand

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

We can use FOIL to expand these brackets.

F – First

\[(FIRST+3)(FIRST+4)\]

\[x \times x = x^2\]

O – Outside

\[(OUTSIDE+3)(x+OUTSIDE)\]

\[x \times 4 = 4x\]

I – Inside

\[(x+INSIDE)(INSIDE+4)\]

\[3 \times x = 3x\]

L – Last

\[(x+LAST)(x+LAST)\]

\[3 \times 4 = 12\]

Add the terms together.

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

Collect the like terms (the 4x and the 3x)

.\[x^2 + 7x +12\]