Multiplying Polynomials
To multiply polynomials, every term of the first must multiply every term of the second. For two binomials that pattern is FOIL; for bigger polynomials it is the same idea, just more terms.
After distributing, combine like terms and write the result in standard form. Careful bookkeeping is the whole game.
Distribute every pair
Multiply each term of the first polynomial by each term of the second. Two binomials give four products (First, Outer, Inner, Last — FOIL).
Add the products, then combine like terms. Larger polynomials produce more products but follow the identical rule.
Watch signs and exponents
When multiplying terms, multiply the coefficients and add the exponents: . Track negative signs carefully.
A missed sign or a wrong exponent is the usual error. Line the products up by degree before combining.
Worked examples
Example 1: two binomials
Multiply .
Answer:
Example 2: monomial times binomial
Multiply .
Answer:
Example 3: binomial times trinomial
Multiply .
Answer:
Try one yourself
Common questions
What does FOIL stand for?
First, Outer, Inner, Last — the four products when multiplying two binomials. It is just organized distribution.
How do I multiply the terms themselves?
Multiply the coefficients and add the exponents: .
Does FOIL work for three-term polynomials?
The name is for binomials, but the principle extends: multiply every term by every term, then combine like terms.
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