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 are a few examples.

$(5x + 3)(2x - 6)$

First we multiply the first terms, $5x$ and $2x$ , yielding $10x^2$ .

Then, the outside terms, $5x$ and $-6$ , giving us $-30x$ .

Next, the inside terms, $3$ and $2x$ , which is $6x$ .

Finally, we multiply the last terms, $-6$ and $3$ , which is $-18$ .

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

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FOIL

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