Multiplication

Example 1 Multiply & simplify.

(4x - 5)(x - 20)

Step 1. Multiply each term in the first binomial through the second binomial.

(4x)(x - 20) + (-5)(x -20)

Step 2. Continue to use the Distributive Property on the two new terms.

(4x)(x) + (4x)(-20) + (-5)(x) + (-5)(-20)

Step 3. Multiply the monomials in each term.

4x² - 80x - 5x + 100

Step 4. Combine like terms if needed and write in standard form.

4x² - 85x + 10

(3x² + 2x - 5)(2x - 3)

Step 1. Multiply each term in the first polynomial through each term in the second.

(3x²)(2x) + (3x²)(-3) + (2x)(2x) + (2x)(-3) + (-5)(2x) + (-5)(-3)

Step 2. Multiply the monomials in each term.

6x³ - 9x² + 4x² - 6x - 10x + 15

Step 4. Combine like terms if needed and write in standard form.

6x³ - 5x² - 16x + 15