Multiplication
4-6Multiplying Polynomials
Overview
Multiply each term of one polynomial by each term of the other. For two binomials, use FOIL.
Key ideas
- FOIL: First, Outer, Inner, Last.
- Combine like terms after distributing.
- Use a table or area model for larger products.
Worked examples
Example 1
Problem. (x + 3)(x − 5)
Solution. x^2 − 5x + 3x − 15 = x^2 − 2x − 15
Example 2
Problem. (2x + 1)(x + 4)
Solution. 2x^2 + 8x + x + 4 = 2x^2 + 9x + 4
Practice
Try each one. Click Show answer when ready.
- 1.
(x + 2)(x + 7)
- 2.
(y − 3)(y − 4)
- 3.
(2a + 5)(a − 1)
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (x + 3)(2x² − x + 4).
- 2.
Simplify (2a − b)(3a + 2b − 1).