How to Multiply a Polynomial and a Monomial? (+FREE Worksheet!)

Related Topics

• How to Multiply Monomials
• How to Multiply and Dividing Monomials
• How to Multiply Binomials
• How to Factor Trinomials
• How to Add and Subtract Polynomials

Step by step guide to Multiplying a Polynomial and a Monomial

• When multiplying monomials, use the product rule for exponents.
• When multiplying a monomial by a polynomial, use the distributive property.
  $\color{blue}{a×(b+c)=a×b+a×c}$

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Multiplying a Polynomial and a Monomial – Example 1:

Multiply expressions. $2x(-2x+4)=$

Solution:

Use Distributive Property: $\color{blue}{a \ (b \ + \ c)=ab \ + \ ac}$

Then: $2x(-2x+4)=-4x^2+8x$

Multiplying a Polynomial and a Monomial – Example 2:

Multiply expressions. $-2x(3x^2+4y^2 )=$

Solution:

Use Distributive Property: $\color{blue}{a \ (b \ + \ c)=ab \ + \ ac}$

Then: $-2x(3x^2+4y^2 )=-6x^3-8xy^2$

Multiplying a Polynomial and a Monomial – Example 3:

Multiply expressions. $-4x(5x+9)=$

Solution:

Use Distributive Property: $\color{blue}{a \ (b \ + \ c)=ab \ + \ ac}$

Then: $-4x(5x+9)=-20x^2-36x$

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Multiplying a Polynomial and a Monomial – Example 4:

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

Solution:

Use Distributive Property: $\color{blue}{a \ (b \ + \ c)=ab \ + \ ac}$

Then: $2x(6x^2-3y^2 )=12x^3-6xy^2$

Exercises for Multiplying a Polynomial and a Monomial

Find each product.

1. $\color{blue}{5 (3x – 6y)}$
2. $\color{ blue }{9x (2x + 4y)}$
3. $\color{blue}{8x (7x – 4)}$
4. $\color{blue}{12x (3x + 9)}$
5. $\color{blue}{11x (2x – 11y)}$
6. $\color{blue}{2x (6x – 6y)}$

Download Multiplying a Polynomial and a Monomial Worksheet

1. $\color{blue}{15x – 30y}$
2. $\color{blue}{18x^2 + 36xy}$
3. $\color{blue}{56x^2 – 32x}$
4. $\color{blue}{36x^2 + 108x}$
5. $\color{blue}{22x^2 – 121xy}$
6. $\color{blue}{12x^2 – 12xy}$

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