How to Multiply a Polynomial and a Monomial? (+FREE Worksheet!)
Learn how to multiply monomials to polynomials using the distributive property and the multiplication property of exponents.
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.
- \(\color{blue}{5 (3x – 6y)}\)
- \(\color{ blue }{9x (2x + 4y)}\)
- \(\color{blue}{8x (7x – 4)}\)
- \(\color{blue}{12x (3x + 9)}\)
- \(\color{blue}{11x (2x – 11y)}\)
- \(\color{blue}{2x (6x – 6y)}\)
Download Multiplying a Polynomial and a Monomial Worksheet
- \(\color{blue}{15x – 30y}\)
- \(\color{blue}{18x^2 + 36xy}\)
- \(\color{blue}{56x^2 – 32x}\)
- \(\color{blue}{36x^2 + 108x}\)
- \(\color{blue}{22x^2 – 121xy}\)
- \(\color{blue}{12x^2 – 12xy}\)
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