Multiplication
Polynomial by a Polynomial
Examples
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
Example 2 Multiply & simplify.
(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