How to Multiply a Polynomial and a Monomial

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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: \(-3x(2x \ - \ 6) \ = \ -6x^2 \ + \ 18x\)

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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) \(22x(x \ - \ 2y \ + \ 9) = \)

Answers

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) \(22x(x \ - \ 2y \ + \ 9) = \)\( \ \color{red}{22x^2 \ - \ 44xy \ + \ 198x}\)

How to Multiply a Polynomial and a Monomial