Monomial Times Polynomial

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

Each product follows the product rule for powers: multiply the coefficients and add the exponents. So $3xx = 3x^{2}$ and $3x\cdot \left(-4\right) = -12x$. The result is $3x\left(x-4\right) = 3x^{2}-12x$.

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 $3xx$, the two factors of $x$ each have the exponent 1, and the exponents add to give $x^{2}$.