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Polynomials

Multiplication

Multiplication of polynomials is also known as "expanding the brackets".   In multiplying two polynomials we will make use of the distributive law: a(b + c) = ab + ac

First let's try multiplying a single term to a polynomial:

3(2x + 5) = 3(2x) + 3(5) = 6x + 15

x(-x + 2) = x(-x) + x(2) = -x2 + 2x

x2(3x + 5) = x2(3x) + x2(5) = 3x3 + 5x2

Exercise 5.

Multiply the two polynomials given, and write your answer with powers in increasing order. Don't type blank spaces in your answer.


Polynomial 1
Polynomial 2
Product

 

 




More generally,

(a +b)(c + d) = a(c + d) +b(c + d)
                       = ac + ad +bc + bd

i.e. we multiply each term in the first brackets by each term in the second brackets and add.


Example 3.

(x^2 + 2)*(3*x + 5) = x^2*(3*x + 5) + 2*(3*x + 5)
=x^2*(3*x)+x^2*(5)+2*(3*x)+2*(5)
=3*x^3+5*x^2+6*x+10.

More Exercises (opens in another window)

Note: The degree of the product of two polynomials is equal to the sum of the degrees of the given polynomials.


Exercise 6.

Multiply the two polynomials given, and write your answer with powers in increasing order. Don't type blank spaces in your answer.


Polynomial 1
Polynomial 2
Product

 

 



 


Example 4.

When one of the given polynomials contains three or more terms it is easier to present the multiplication as follows.

Multiply :

A visual representation is shown. (3*x+5)*(x^2+x-2)=3*x^3+8*x^2-x-10.

More Exercises (opens in another window)

Exercise 7.

Multiply the two polynomials given, and write your answer with powers in increasing order. Don't type blank spaces in your answer.


Polynomial 1
Polynomial 2
Product

 

 



 

<< Subtracting Polynomials | Polynomials Index | Division of Polynomials >>

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