Now that we know what a polynomial is, we can use the distributive property to multiply (expand) polynomials. To multiply polynomials, we multiply each term of one expression by each term in another expression. This section will show you how to multiply a polynomial by a monomial and multiply a binomial by a binomial using the distributive property and product rule of exponents.
Click on the titles below to view each example.
Example 1. Multiply the expression negative 2x times open parenthesis 5x squared plus 7x minus 3 close parenthesis.
Line 1: Multiply negative 2x by each term inside the parentheses, so the expression is negative 2x times 5x squared plus negative 2x times 7x minus negative 2x times 3
Line 2: Multiply to simplify the expression to negative 10x cubed minus 14x squared plus 6x.
Example 2. Multiply the expression open parenthesis 4y plus 3 close parenthesis times open parenthesis 6y minus 5 close parenthesis.
Line 1: Multiply each term in the first set of parentheses by each term inside the second set of parentheses, so the expression is 4y times 6y plus 4y times negative 5 plus 3 times 6y plus 3 times negative 5.
Line 2: Multiply to simplify the expression to 24y squared minus 20y plus 18y minus 15.
Line 3: Collect like terms, so the final expression is 24y squared minus 2y minus 15.
Examples Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window