Overview
This lecture explains how to multiply binomials using the FOIL method, with step-by-step examples and tips for handling tricky cases.
The FOIL Method Explained
- The FOIL method stands for First, Outer, Inner, Last and is used to multiply two binomials.
- To use FOIL, multiply each term in the first binomial by each term in the second binomial.
Example: Basic Binomial Multiplication
- Example: Multiply (x + 2)(2x + 3) using FOIL.
- First: x × 2x = 2x².
- Outer: x × 3 = 3x.
- Inner: 2 × 2x = 4x.
- Last: 2 × 3 = 6.
- Combine all terms: 2x² + 3x + 4x + 6.
- Combine like terms: 2x² + 7x + 6.
Example: Squaring a Binomial
- To square (3x + 4), write as (3x + 4)(3x + 4).
- Apply FOIL: First: 3x × 3x = 9x².
- Outer and Inner (both): 3x × 4 = 12x, 4 × 3x = 12x (sum = 24x).
- Last: 4 × 4 = 16.
- Combine: 9x² + 12x + 12x + 16 = 9x² + 24x + 16.
Example: Binomials with Negatives
- Example: (x + 1)(2x - 3).
- First: x × 2x = 2x².
- Outer: x × (-3) = -3x.
- Inner: 1 × 2x = 2x.
- Last: 1 × (-3) = -3.
- Combine: 2x² - 3x + 2x - 3.
- Combine like terms: 2x² - x - 3.
Key Terms & Definitions
- Binomial — An algebraic expression with two terms (e.g., x + 2).
- FOIL Method — Technique for multiplying two binomials: First, Outer, Inner, Last.
- Combine Like Terms — Add or subtract terms with the same variable and exponent.
Action Items / Next Steps
- Practice multiplying binomials using the FOIL method.
- Review and complete any assigned problems on binomial multiplication.