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