# Multiplying Binomial Terms

$(x+2)(x-1$)

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

$(a+b)(c+d)$

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

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$! – amWhy May 18 '11 at 18:14 ## 2 Answers It's not wrong. You just haven't noticed that$-x+2x = x, so that, if you simplify, you get $$(x+2)(x-1) = x^2 -x + 2x - 2 = x^2 + x - 2.$$ - I see, thanks for helping out, finally I can continue my studies. Appreciate it ;) – Muazam May 18 '11 at 17:57 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. - 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