Difference between revisions of "FOIL"
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Latest revision as of 12:34, 14 July 2021
FOIL, standing for first, outside, inside, last, is a mnemonic device for remembering the distributive property when two binomials are multiplied.
![\[(a+b)(c+d) = ac + ad + bc + bd\]](http://latex.artofproblemsolving.com/a/d/9/ad98d8c02772c1e5c65429103a2b7863f5aa6834.png)
Here is an example.
![\[(5x + 3)(2x - 6)\]](http://latex.artofproblemsolving.com/8/4/5/8456db0370eb03e221ce00a55085317ff72b38a0.png)
First we multiply the first terms ![\[5x \times 2x = 10x^2\]](http://latex.artofproblemsolving.com/8/6/f/86f046471e5f37ca0458749d16bd41a86a74cc2b.png)
Then, the outside terms ![\[5x \times -6 = -30x\]](http://latex.artofproblemsolving.com/6/7/5/6758adcf244f9e54417fdc15a4b80c69ecabedc5.png)
Next, the inside terms ![\[3 \times 2x = 6x\]](http://latex.artofproblemsolving.com/9/d/4/9d410a08e68d9b7e6ffe8fc18b2d5657b88fddda.png)
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Finally, we multiply the last terms ![\[-6 \times 3 = -18\]](http://latex.artofproblemsolving.com/8/7/8/878050edf35b549446bab317c228059124088bc6.png)
Thus, our answer is ![\[10x^2 - 30x + 6x - 18\]](http://latex.artofproblemsolving.com/e/2/0/e20fce512988333112c993161673cc78bc420cb6.png)
, which, when simplified, gives us a final answer of ![\[\boxed{10x^2 - 24x - 18}\]](http://latex.artofproblemsolving.com/b/e/2/be23574c0413243f3ab5cc07a3a49f134adfe98d.png)
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