Multiplying Binomial Terms

Question

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

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!

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).
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...
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 $(a + b)^2 = a^2 + b^2$!

Arturo Magidin · Accepted Answer · 2011-05-18 17:53:53Z

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 $$(x+2)(x-1) = x^2 -x + 2x - 2 = x^2 + x - 2.$$

answered May 18 '11 at 17:53

Arturo Magidin
158k14250501

I see, thanks for helping out, finally I can continue my studies. Appreciate it ;) – Muazam May 18 '11 at 17:57

JavaMan · Answer 2 · 2011-05-28 16:49:40Z

up vote 3 down vote

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.

edited May 28 '11 at 16:49

answered May 18 '11 at 18:00

JavaMan
8,30911633

	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

2 Answers