Algebra
Polynomials
Multiplying polynomials
20 practice questions
2 video lessons
Theory + worked examples
Theory
To multiply polynomials, multiply every term of one by every term of the other, then combine like terms:
- Monomial × polynomial: distribute.
- Binomial × binomial: FOIL (First, Outer, Inner, Last).
- Larger products: distribute each term.
Every term multiplies every term — miss none.
An area model for \((x+2)(x+3)\).
Multiplying strategies.
FOIL:
\[(a+b)(c+d)=ac+ad+bc+bd\]
Combine like terms after multiplying.
How to multiply
- Multiply each term of the first factor by each of the second.
- Track the signs.
- Combine like terms.
- Write in standard form.
Example 1 — Monomial times binomial
Multiply \(2x(3x+4)\).
Solution
Distribute.
| \(2x(3x+4)\) | \(=\) | \(6x^2+8x\) |
Example 2 — FOIL
Multiply \((x+2)(x+3)\).
Solution
Multiply each pair, then combine.
| \(x^2+3x+2x+6\) | ||
| \(=\) | \(x^2+5x+6\) |
Example 3 — A difference
Multiply \((2x-1)(x+4)\).
Solution
FOIL with signs.
| \(2x^2+8x-x-4\) | ||
| \(=\) | \(2x^2+7x-4\) |
Example 4 — Binomial times trinomial
Multiply \((x+1)(x^2+2x+3)\).
Solution
Distribute each term.
| \(x^3+2x^2+3x+x^2+2x+3\) | ||
| \(=\) | \(x^3+3x^2+5x+3\) |
Common pitfalls
Multiply every pair — don't miss the middle terms.
Add exponents when multiplying variables.
Combine like terms at the end.
Frequently asked questions
How do you multiply two binomials?
Use FOIL, then combine like terms.
Multiply \(3x(x+2)\).
\(3x^2+6x\).
What does FOIL stand for?
First, Outer, Inner, Last.
Do you combine like terms after?
Yes.
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