Quadratics: Multiplying Polynomials
A free College Algebra lesson from the “Quadratics: Multiplying and Factoring” unit, with a worked example and practice problems including step-by-step solutions.
Quadratic products come from multiplying binomials, such as (x + 2)(x + 5). Each term in one factor must multiply each term in the other factor. This process explains where quadratic trinomials come from: the first terms create the x^2 term, the outer and inner products combine to create the middle term, and the constants create the final term. This matters because expanding and factoring are inverse skills. When practicing, distribute systematically and combine like terms. A common mistake is multiplying only the first and last terms and forgetting the middle products.
What you'll learn
- Multiply binomials
- Use special product patterns
- Connect products to quadratic form
Worked example
Problem. Expand (x + 4)(x - 7).
- Multiply first, outer, inner, last.
- x^2 - 7x + 4x - 28.
- Combine like terms to get x^2 - 3x - 28.
Answer: x^2 - 3x - 28
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice and typed response). Counts include repeated prompts and variants.
Practice problems
1. Expand (x + 2)(x + 6).
Choices: x^2 + 8x + 12 · x^2 + 12 · x^2 + 4x + 12 · 2x + 8
Show solution
- The middle terms add to 8x.
Answer: x^2 + 8x + 12
2. Expand (x - 5)^2.
Choices: x^2 - 10x + 25 · x^2 - 25 · x^2 + 10x + 25 · x^2 - 5x + 25
Show solution
- Square both terms and double the product.
Answer: x^2 - 10x + 25
3. Expand (2x + 3)(x - 4).
Choices: 2x^2 - 5x - 12 · 2x^2 - 8x + 3 · 2x^2 + 11x - 12 · 3x^2 - x - 12
Show solution
- The middle terms are -8x and 3x.
Answer: 2x^2 - 5x - 12
4. Expand (x + 7)(x - 1).
Choices: x^2 + 6x - 7 · x^2 - 8x - 7 · x^2 + 7x - 1 · x^2 - 7
Show solution
- The middle terms are -x and 7x.
Answer: x^2 + 6x - 7
5. Expand (3x - 2)(x + 5).
Choices: 3x^2 + 13x - 10 · 3x^2 + 15x - 10 · 3x^2 - 7x - 10 · 4x^2 + 3x - 10
Show solution
- The middle terms are 15x and -2x.
Answer: 3x^2 + 13x - 10
Practice this interactively with instant feedback and an AI tutor.
Practice Quadratics: Multiplying Polynomials Take the free placement check