## How to Multiply a Polynomial and a Monomial

In order to multiply a polynomial by a monomial, you would utilize the distributive property: multiply each of the terms of the polynomial by the monomial. That means you must multiply the coefficients and add in the exponents of the applicable variables.

### Bit by Bit guide for Multiplying a Polynomial and a Monomial

• Whenever you multiply monomials, you must utilize the product rule for exponents.
• Whenever you multiply a monomial by a polynomial, you must utilize the distributive property.
$$a \times (b \ + \ c) \ = \ a \times b \ + \ a \times c$$

#### Multiplying Polynomials and Monomials – Example one:

Multiply expressions.
$$-3x(2x \ - \ 6) \ =$$

Answer: Utilize the Distributive Property: $$a \times (b \ + \ c) \ = \ a \times b \ + \ a \times c$$ Then: $$-3x(2x \ - \ 6) \ = \ -6x^2 \ + \ 18x$$

## Multiply a Polynomial and a Monomial Video

### Exercises for Multiplying a Polynomial and a Monomial

1) $$12(x \ + \ 2) =$$

2) $$19(x \ + \ 2) =$$

3) $$-21x(x \ + \ 2) =$$

4) $$-14x(x \ + \ 3) =$$

5) $$18x(x \ - \ 2y) =$$

6) $$10x(x \ - \ 3y) =$$

7) $$3x(x \ - \ 4y) =$$

8) $$14x(x \ - \ 4y \ + \ 4) =$$

9) $$7x(x \ - \ 2y \ + \ 5) =$$

10) $$22x(x \ - \ 2y \ + \ 9) =$$

1) $$12(x \ + \ 2) =$$$$\ \color{red}{12x \ + \ 24}$$
2) $$19(x \ + \ 2) =$$$$\ \color{red}{19x \ + \ 38}$$
3) $$-21x(x \ + \ 2) =$$$$\ \color{red}{-21x^2 \ + \ 42x}$$
4) $$-14x(x \ + \ 3) =$$$$\ \color{red}{-14x^2 \ + \ 42x}$$
5) $$18x(x \ - \ 2y) =$$$$\ \color{red}{18x^2 \ - \ 36xy}$$
6) $$10x(x \ - \ 3y) =$$$$\ \color{red}{10x^2 \ - \ 30xy}$$
7) $$3x(x \ - \ 4y) =$$$$\ \color{red}{3x^2 \ - \ 12xy}$$
8) $$14x(x \ - \ 4y \ + \ 4) =$$$$\ \color{red}{14x^2 \ - \ 56xy \ + \ 56x}$$
9) $$7x(x \ - \ 2y \ + \ 5) =$$$$\ \color{red}{7x^2 \ - \ 14xy \ + \ 35x}$$
10) $$22x(x \ - \ 2y \ + \ 9) =$$$$\ \color{red}{22x^2 \ - \ 44xy \ + \ 198x}$$

## Multiplying a Polynomial and a Monomial Practice Quiz

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