Math
Multiplying polynomials.
Definition
The process of multiplying two or more polynomials by distributing each term of one polynomial to every term of the other, then combining like terms. For binomials, the FOIL method (First, Outer, Inner, Last) is a common shortcut.
How it works · 4 phases
Step by step.
- Distribute each term of the first polynomial to every term of the second.
- Multiply the coefficients and add the exponents of like bases.
- Combine like terms.
- Write the result in standard form (descending order of degree).
Examples
Real-world.
- 1 (x + 3)(x + 5) = x² + 8x + 15 using FOIL
- 2 (2x − 1)(x² + 3x + 4) = 2x³ + 6x² + 8x − x² − 3x − 4 = 2x³ + 5x² + 5x − 4
- 3 (a + b)² = a² + 2ab + b²
Key Fact
FOIL: (a+b)(c+d) = ac + ad + bc + bd