Difference between revisions of "FOIL"

Revision as of 12:02, 16 August 2008

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 $5x \times 2x = 10x^2$

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 $\boxed{10x^2 - 24x - 18}$ .

@@ Line 7: / Line 7: @@
 <cmath>(5x + 3)(2x - 6)</cmath>
-First we multiply the first terms, <cmath>5x</cmath> and <cmath>2x</cmath>, yielding <cmath>10x^2</cmath>.
+First we multiply the first terms <cmath>5x \times 2x = 10x^2</cmath>
-Then, the outside terms, <cmath>5x</cmath> and <cmath>-6</cmath>, giving us <cmath>-30x</cmath>.
+Then, the outside terms <cmath>5x \times -6 = -30x</cmath>
-Next, the inside terms, <cmath>3</cmath> and <cmath>2x</cmath>, which is <cmath>6x</cmath>.
+Next, the inside terms <cmath>3 \times 2x = 6x</cmath>.
-Finally, we multiply the last terms, <cmath>-6</cmath> and <cmath>3</cmath>, which is <cmath>-18</cmath>.
+Finally, we multiply the last terms <cmath>-6 \times 3 = -18</cmath>
 Thus, our answer is <cmath>10x^2 - 30x + 6x - 18</cmath>, which, when simplified, gives us a final answer of <cmath>\boxed{10x^2 - 24x - 18}</cmath>.
@@ Line 22: / Line 22: @@
 [[Category:Elementary algebra]]
-{{stub}}

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Difference between revisions of "FOIL"

Revision as of 12:02, 16 August 2008

See also