Sign In | Subscribe
INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
Start learning today, and be successful in your academic & professional career. Start Today!
Loading video...
This is a quick preview of the lesson. For full access, please Log In or Sign up.
For more information, please see full course syllabus of Algebra 1
  • Discussion

  • Study Guides

  • Practice Questions

  • Download Lecture Slides

  • Table of Contents

  • Related Books

Bookmark and Share

Start Learning Now

Our free lessons will get you started (Adobe Flash® required).
Get immediate access to our entire library.

Sign up for Educator.com

Membership Overview

  • Unlimited access to our entire library of courses.
  • Search and jump to exactly what you want to learn.
  • *Ask questions and get answers from the community and our teachers!
  • Practice questions with step-by-step solutions.
  • Download lesson files for programming and software training practice.
  • Track your course viewing progress.
  • Download lecture slides for taking notes.
  • Learn at your own pace... anytime, anywhere!

Multiplying Polynomials by Monomials

  • Use the distributive property to multiply a polynomial by a monomial.
  • You can solve many equations by multiplying polynomials by monomials and adding and subtracting polynomials. Often these equations simplify to linear equations that can be solved using the methods used to solve linear equations.

Multiplying Polynomials by Monomials

Multiply:
2m2( 4m3 − 5m4 + 6m2 )
  • 2m2( 4m3 ) + 2m2( − 5m4 ) + 2m2( 6m2 )
8m5 − 10m6 + 12m4
Multiply:
5h3( 3h6 + 7h3 − 12h4 )
  • 5h3( 3h6 ) + 5h3( 7h3 ) + 5h3( − 12h4 )
15h9 + 35h6 − 60h7
Multiply:
6y7( 11y2 − 14y7 − 9y10 )
  • 6y7( 11y2 ) + 6y7( − 14y7 ) + 6y7( − 9y10 )
66y9 − 84y14 − 54y17
Multiply:
4k4( 9k3 + 11k6 − 7k5 )
  • 4k4( 9k3 ) + 4k4( 11k6 ) + 4k4( − 7k5 )
36k7 + 44k10 − 28k9
Simplify:
2m( 5m4 − 9m + 7m5 ) − 4m3( 6m3 + 4m2 )
  • ( 2m )( 5m4 ) + ( 2m )( − 9m ) + ( 2m )( 7m5 ) + ( − 4m3 )( 6m3 ) + ( − 4m3 )( 4m2 )
  • 10m5 − 18m2 + 14m6 − 24m6 − 16m5
  • ( 10m5 − 16m5 ) − 18m2 + ( 14m6 − 24m6 )
  • − 6m5 − 18m2 − 10m6
− 10m6 − 6m5 − 18m2
Simplify:
5j2( 7j − 3j2 ) + 6j( 4j4 − 8j2 + 2j )
  • ( 5j2 )( 7j ) + ( 5j2 )( − 3j2 ) + ( 6j )( 4j4 ) + ( 6j )( − 8j2 ) + ( 6j )( 2j )
  • 35j3 − 15j4 + 24j5 − 48j3 + 12j2
  • ( 35j3 − 48j3 ) − 15j4 + 24j5 + 12j2
  • − 13j3 − 15j4 + 24j5 + 12j2
24j5 − 15j4 − 13j3 + 12j2
Simplify:
6x(3x2 + 4x − 10x5) + 4x(7x2 − 8x + 2x) − (3x3 − 2x5 + 5x)
  • ( 6x )( 3x2 ) + ( 6x )( 4x ) + ( 6x )( − 10x5 ) + ( 4x )( 7x2 ) + ( 4x )( 2x ) + ( − 3x )( x3 ) + ( − 3x )( − 2x5 ) + ( − 3x )( 5x )
  • 18x3 + 24x2 − 60x6 + 28x3 − 32x2 + 8x2 − 3x4 + 6x6 − 15x2
  • ( 18x3 + 28x3 ) + ( 24x2 − 32x2 + 8x2 − 15x2 ) + ( − 60x6 + 6x6 ) − 3x4
  • 46x3 − 15x2 − 54x6 − 3x4
− 54x6 − 3x4 + 46x3 − 15x2
Simplify:
3y2( y2 + 4y − 9y3 ) − 7y( − 10y2 + 3y3 ) + 4y3( 4y11 )
  • ( 3y2 )( y2 ) + ( 3y2 )( 4y ) + ( 3y2 )( − 9y3 ) + ( − 7y )( − 10y2 ) + ( − 7y )( − 3y3 ) + ( 4y3 )( 4y11 )
  • 3y4 + 12y3 − 27y5 + 70y3 − 21y4 + 16y14
16y14 − 27y5 − 18y4 + 82y3
Solve:
4k( 2k + 3 ) − 5( k ) = − 2k( 3k − 6 ) − 10
  • 8k2 + 12k − 5k2 = − 6k2 + 12k − 10
  • 3k2 + 12k = − 6k2 + 12k − 10
  • 9k2 = − 10
  • [(9k2)/9] = [10/9]
  • k2 = [10/9]
k = √{[10/9]}
Solve:
5m( 2m − 3 ) + 8 = 3m( 2m + 8 ) − m( − 4m + 1 )
  • 10m2 − 15m + 8 = 6m2 + 24m + 4m2 − m
  • 10m2 − 15m + 8 = 10m2 − 23m
  • − 15m + 8 = − 23m
  • 8 = − 8m
m = − 1

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Multiplying Polynomials by Monomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Distributive Property 0:07
    • Example
  • Solving Equations 1:36
    • Isolate Variable and Solve
  • Example 1: Multiply 1:59
  • Example 2: Simplify 3:33
  • Example 3: Simplify 7:20
  • Example 4: Solve 13:37