Multiplying a polynomial by a monomial

To multiply a polynomial by a monomial, we multiply every term of the polynomial by that monomial and add the products; this rests on the distributive law: (a + b + c)m = am + bm + cm. Each product is found by the rule for multiplying monomials: coefficients are multiplied and exponents of equal letters are added. The result is again a polynomial, and we write it in standard form. We watch the signs: multiplying by a negative monomial changes the sign of every term. Multiplying a monomial by a polynomial is done in the same way, since changing the order of factors does not change the product.