The easiest case of polynomial multiplication is multiplying a monomial and a polynomial. In this case, we "distribute" the monomial to each term in the polynomial. We really do distribute it, though. We weren't using the quotation marks to be sarcastic or ironic.
Sample Problem
What is (2x)(3x2 + 4x + 9)?
We use the distributive property to distribute (2x) over the longer polynomial, then simplify the resulting terms.
| (2x)(3x2 + 4x + 9) | = | (2x)(3x2) + (2x)(4x) + (2x)(9) |
| = | 6x3 + 8x2 + 18x |
Sample Problem
What is (5x2)(4x3 + 7x)?
We distribute (5x2) over both terms in the second set of parentheses, then simplify.
(5x2)(4x3) + (5x2)(7x) =
20x5 + 35x3