Expanding Quadratic Brackets

Video masterclass

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)

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

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