Overview
This lecture explains how to multiply two binomials using the distributive method and how to combine like terms to simplify the result.
Multiplying Binomials
- Binomials are algebraic expressions with two terms.
- To multiply two binomials, multiply each term in the first bracket by each term in the second bracket.
- The process ensures all terms in one bracket are distributed to all terms in the other bracket.
Step-by-Step Example 1: (x - 3)(x + 2)
- x × x = x².
- x × 2 = 2x.
- -3 × x = -3x.
- -3 × 2 = -6.
- Combine like terms: 2x and -3x → 2x - 3x = -1x.
- Final result: x² - 1x - 6.
Step-by-Step Example 2: (x + 7)(x + 2)
- x × x = x².
- x × 2 = 2x.
- 7 × x = 7x.
- 7 × 2 = 14.
- Combine like terms: 2x and 7x → 2x + 7x = 9x.
- Final result: x² + 9x + 14.
Key Terms & Definitions
- Binomial — An algebraic expression with exactly two terms (example: x + 2).
- Like Terms — Terms that have the same variable part and can be combined (example: 2x and -3x).
- Distributive Property — Multiplying each term in one expression by each term in another.
Action Items / Next Steps
- Practice multiplying different binomials and combining like terms.
- Review and memorize steps for multiplying binomials for future problems.