# 10.4 – Polynomial Multiplication

## Key Terms

• Column – A vertical list of numbers of other information in a table.

## Review

Remember…
• Rule: To multiply any two polynomials, multiply each term in one polynomial by each term in the other.

## Notes

Polynomial Multiplication Using Tables
• You can create a table to help you organize polynomials for multiplication
• How to Use a Table to Multiply Two Polynomials
• Step 1: Use the terms in one polynomial to label the columns (one term per column).
• Step 2: Label the rows with the terms in the other polynomial (one term per row).
• Step 3: Multiply each column label and row label to fill in all the entries.
• Step 4: Add all the products in the entries.
• Step 5: Simplify the sum, if possible.

• Example 1
• Example 2

The Distributive Property
•  How to Use the Distributive Property to Multiply Polynomials
• Step 1: Distribute the first polynomial over the second one.
• Step 2: Use the distributive property again on the smaller products.
• Step 3: Collect like terms and simplify the answer.

Multiplying Polynomials Vertically
• How to Multiply Two Binomials Vertically
• Step 1: Multiply each term in the top binomial by the last term in the bottom binomial.
• Step 2: Multiply each term in the top binomial by the first term in the bottom binomial.
• Step 3: Add the two smaller products.

• Example

• Another Example

## Examples

 Ex 1. Use a table to compute the product: $(6x^{2}-3x-6)(3x+6)$ Ex 2. Use a table to compute the product: $(5x^{2}-4x-5)(4x+7)$ Ex 3. Use a table to compute the product: $(4x^{2}-2x-4)(7x^{2}+8x+7)$