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Totally forgot how to do it. Isn't this the rule:


$a*c +a*d +b*c +b*d$

The answer I'm getting is $x^2-x+2x-2$ which is wrong. Please help me out, thanks!

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One mnemonic that might also help you recall how to multiply binomials (two terms in parentheses) is FOIL: First terms: $x^2$; Outer terms: $-x$; Inner terms: $2x$; Last terms: $-2$. The key fact to remember, as you do above, to *distribute$ each value of one term by multiplying it with each of the values of the second term (which can be generalized to non-binomial factors). –  amWhy May 18 '11 at 18:00
Personally, I find FOIL rather foolish (or "foilish", perhaps?) a mnemonic; distributivity is better, and less likely to confuse the student when you need to multiply binomial by a trinomial, or more complex expressions... –  Arturo Magidin May 18 '11 at 18:07
yes, indeed, "foil"-ish! I agree that emphasizing distributivity is more generalizable. "FOIL" can simply be a reminder of the need to distribute multiplication, for those who insist, e.g., that $(a + b)^2 = a^2 + b^2$! –  amWhy May 18 '11 at 18:14
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2 Answers 2

up vote 8 down vote accepted

It's not wrong. You just haven't noticed that $-x+2x = x$, so that, if you simplify, you get $$(x+2)(x-1) = x^2 -x + 2x - 2 = x^2 + x - 2.$$

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I see, thanks for helping out, finally I can continue my studies. Appreciate it ;) –  Muazam May 18 '11 at 17:57
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The FOIL "rule" (First, Outer, Inner, Last) simply follows from the distributive laws:

$$k(m+n) = km + kn$$

$$(k+m)n = kn + mn$$

In your case,

$$ \begin{align} (x+2)(x-1) = x(x-1) + 2(x-1) = x^2 - x + 2x - 2 = x^2 + x - 2, \end{align} $$

as you have already noted.

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Well, to be strictly accurate, you also need commutativity — or, equivalently, the law that $(m+n)k = mk + nk$ (which is what you used in the first step). –  ShreevatsaR May 28 '11 at 15:32
@ShreevatsaR: Thanks for the comment. I edited my answer accordingly. –  JavaMan May 30 '11 at 21:27
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