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FOIL

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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

Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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