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.

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

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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.
    \(\color{blue}{a×(b+c)=a×b+a×c} \)

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

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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