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.

What is (2*x*)(3*x*^{2} + 4*x* + 9) ?

We use the distributive property to distribute (2*x*) over the longer polynomial, then simplify the resulting terms.

(2x)(3x^{2} + 4x + 9) | = | (2x)(3x^{2}) + (2x)(4x) + (2x)(9) |

= | 6x^{3} + 8x^{2} + 18 |

What is (5*x*^{2})(4*x*^{3} + 7*x*)?

We distribute (5*x*^{2}) to find (5*x*^{2})(4*x*^{3}) + (5*x*^{2})(7*x*),

which simplifies to 20*x*^{5} + 35*x*^{3}.

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