Expanding Quadratic Brackets

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

For simple brackets:

$(a + b) (c + d) = a c + a d + b c + b d$

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

We can use FOIL to expand these brackets.

F - First

$(F I R S T + 3) (F I R S T + 4)$

$x \times x = x^{2}$

O - Outside

$(O U T S I D E + 3) (x + O U T S I D E)$

$x \times 4 = 4 x$

I - Inside

$(x + I N S I D E) (I N S I D E + 4)$

$3 \times x = 3 x$

L - Last

$(x + L A S T) (x + L A S T)$

$3 \times 4 = 12$

Add the terms together.

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

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

. $x^{2} + 7 x + 12$

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