Monomial Times Polynomial

The distributive property, a(b + c) = ab + ac, works when the multiplier is a monomial, not only when it is a number. To expand 3x(x - 4), multiply each term inside the parentheses by 3x.

Each product follows the product rule for powers: multiply the coefficients and add the exponents. So 3x * x = 3x^2 and 3x * (-4) = -12x. The result is 3x(x - 4) = 3x^2 - 12x.

To multiply a monomial by a polynomial, use two rules you already know. First, distribute the monomial to every term inside the parentheses. Then, for each product, multiply the coefficients and add the exponents. In 3x * x, the two factors of x each have the exponent 1, and the exponents add to give x^2.