Multiplying Binomials and Polynomials
Multiplying binomials or polynomials can look like a daunting
task, but it really isn’t. It’s actually pretty mindless. The most
important thing is to be careful that you haven’t forgotten a term
somewhere.
Binomials
Problems that require you to multiply binomials are pretty
common on the SAT. This is not a difficult task if you remember
the acronym FOIL, which stands for First Outer Inner Last. For example,
if you must multiply the binomials (x + 1)(x +
3) you start by multiplying the first number in each polynomial (x)(x),
then the outer numbers (x)(3), then
the inner numbers (1)(x), and finally
the last numbers (1)(3) and you get:
The only tricky part to following FOIL is remembering
to pay attention to signs. For instance, if you have the polynomials (x +
1)(x – 3), then the –3 comes
to play an important role. You always add up the products of FOIL,
but look what happens when there’s a negative number involved:
There are a few standard binomials that ETS includes in
almost every SAT. You should memorize how to multiply these binomials:
Polynomials
On extremely rare occasions, a question on the SAT might
ask you to multiply polynomials. For example, you might be asked
to multiply the polynomial (a + b + c) by
the binomial (d + e).
To carry out this multiplication, you should treat the larger polynomial
as a single term and distribute the smaller one across it:
To multiply (2x + 3)(x2 +
4x + 7):
Then combine like terms to get your final answer:
(x-3).gif)
(a+B+c).gif)
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