We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

Обучение Руководства > Prealgebra

Multiplying a Polynomial by a Monomial

Learning Outcomes

  • Multiply a polynomial by a monomial using the distributive property
  In Distributive Property you learned to use the Distributive Property to simplify expressions such as 2(x−3)2\left(x - 3\right). You multiplied both terms in the parentheses, x and 3x\text{ and }3, by 22, to get 2x−62x - 6. With this chapter's new vocabulary, you can say you were multiplying a binomial, x−3x - 3, by a monomial, 22. Multiplying a binomial by a monomial is nothing new for you!  

example

Multiply: 3(x+7)3\left(x+7\right). Solution
3(x+7)3\left(x+7\right)
Distribute. .
3⋅x+3⋅73\cdot x+3\cdot 7
Simplify. 3x+213x+21
 

try it

[ohm_question]146197[/ohm_question]
   

example

Multiply: x(x−8)x\left(x - 8\right).

Answer: Solution

x(x−8)x(x-8)
Distribute. .
x2−8xx^2-8x
Simplify. x2−8xx^2-8x

 

try it

[ohm_question]146198[/ohm_question]
   

example

Multiply: 10x(4x+y)10x\left(4x+y\right).

Answer: Solution

10x(4x+y)10x(4x+y)
Distribute. .
10x⋅4x+10x⋅y10x\cdot{4x}+10x\cdot{y}
Simplify. 40x2+10xy40x^2+10xy

 

try it

[ohm_question]146201[/ohm_question]
  Multiplying a monomial by a trinomial works in much the same way.  

example

Multiply: −2x(5x2+7x−3)-2x\left(5{x}^{2}+7x - 3\right).

Answer: Solution

−2x(5x2+7x−3)-2x\left(5{x}^{2}+7x - 3\right)
Distribute. .
−2x⋅5x2+(−2x)⋅7x−(−2x)⋅3-2x\cdot 5{x}^{2}+\left(-2x\right)\cdot 7x-\left(-2x\right)\cdot 3
Simplify. −10x3−14x2+6x-10{x}^{3}-14{x}^{2}+6x

 

try it

[ohm_question]146203[/ohm_question]
   

example

Multiply: 4y3(y2−8y+1)4{y}^{3}\left({y}^{2}-8y+1\right).

Answer: Solution

4y3(y2−8y+1)4{y}^{3}\left({y}^{2}-8y+1\right)
Distribute. .
4y3⋅y2−4y3⋅8y+4y3⋅14{y}^{3}\cdot {y}^{2}-4{y}^{3}\cdot 8y+4{y}^{3}\cdot 1
Simplify. 4y5−32y4+4y34{y}^{5}-32{y}^{4}+4{y}^{3}

 

try it

[ohm_question]146204[/ohm_question]
  Now we will have the monomial as the second factor.  

example

Multiply: (x+3)p\left(x+3\right)p.

Answer: Solution

(x+3)p\left(x+3\right)p
Distribute. .
x⋅p+3⋅px\cdot p+3\cdot p
Simplify. xp+3pxp+3p

 

try it

[ohm_question]146206[/ohm_question]
In the following video we show more examples of how to multiply monomials with other polynomials. https://youtu.be/bwTmApTV_8o

Licenses & Attributions