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Multiplication of a Polynomial by a Monomial Help

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By — McGraw-Hill Professional
Updated on Sep 8, 2011

Multiplication of a Polynomial by a Monomial

When a polynomial is multiplied by a monomial, the distributive property is used. Recall from Chapter 7 that the distributive property states that a(b + c) = a · b + a · c.

To multiply a polynomial by a monomial, multiply each term in the polynomial by the monomial .

Examples

Example 1

Multiply x(2x + 3y).

Solution 1

Multiplication of a Polynomial by a Monomial

Example 2

Multiply 5x 2 y(3x + 2y - 6)

Solution 2

Multiplication of a Polynomial by a Monomial

Multiplication of a Polynomial by a Monomial Practice Problems

Practice

Multiply:

  1. 8(2x + 2y - 6)
  2. 4x(5x 2 - 6x 2 - 12)
  3. -3xy 2 (2xy +6x 2 -10)
  4. -c 2 d 3 (3c 2 + 4cd - 5d 2 )
  5. 6ab(3a - 2b + 4c 2 )

Answers

  1. 16x + 16y - 48
  2. 20x 3 - 24x 2 + 48x
  3. -6x 2 y 3 - 18x 3 y 2 + 30xy 2
  4. -3c 4 d 3 -4c 3 d 4 + 5c 2 d 5
  5. 18a 2 b - 12ab 2 + 24abc 2

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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