FOIL

FOIL, standing for first, outside, inside, last, is a mnemonic device for remembering the distributive property when two binomials are multiplied.

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

Here is an example.

\[(5x + 3)(2x - 6)\]

First we multiply the first terms \[5x \times 2x = 10x^2\]

Then, the outside terms \[5x \times -6 = -30x\]

Next, the inside terms \[3 \times 2x = 6x\].

Finally, we multiply the last terms \[-6 \times 3 = -18\]

Thus, our answer is \[10x^2 - 30x + 6x - 18\], which, when simplified, gives us a final answer of \[\boxed{10x^2 - 24x - 18}\].

See also