Lesson 26: Multiplying Polynomials (Distributive Property, FOIL)

Multiplying polynomials involves using the distributive property to multiply each term in one polynomial by each term in the other. For binomials, we often use the FOIL method (First, Outer, Inner, Last) as a shortcut.

Using the Distributive Property

Example: (2x + 3)(x² + 4)

Step 1: Multiply each term in the first polynomial by each term in the second:

2x * x² = 2x³

2x * 4 = 8x

3 * x² = 3x²

3 * 4 = 12

Step 2: Combine all terms:

Answer: 2x³ + 3x² + 8x + 12

FOIL Method for Binomials

FOIL stands for First, Outer, Inner, Last. It is used for multiplying two binomials.

Example: (x + 5)(x − 2)

1. First: x * x = x²
2. Outer: x * (−2) = −2x
3. Inner: 5 * x = 5x
4. Last: 5 * (−2) = −10

Combine like terms: x² − 2x + 5x − 10 = x² + 3x − 10

Practice Problems

1. (x + 3)(x + 4)
2. (2x − 5)(x + 7)
3. (x + 2)(x² − x + 3)
4. (3x − 1)(2x² + x − 4)