# Polynomials of 9th Grade

• Aug 3rd 2009, 06:24 PM
tecktonikk
Polynomials of 9th Grade
Use these patterns to factor polynimials that are sums and differences of cubes:
a^3 + b^3 = (a+b)(a^2-ab+b^2)
a^3 - b^3 = (a-b)(a^2-ab+b^2)

1. x^3 + 8
2. 8x^3 + 27
3. 64 - y^3
4. 2u^3 +16v^3
5. d^6 + f^3
6. w^6 - 1

Please, show work!!! :)
Thank You so so much!!
• Aug 3rd 2009, 06:33 PM
Chris L T521
Quote:

Originally Posted by tecktonikk
Use these patterns to factor polynimials that are sums and differences of cubes:
a^3 + b^3 = (a+b)(a^2-ab+b^2) --- (1)
a^3 - b^3 = (a-b)(a^2-ab+b^2) --- (2)

1. x^3 + 8

Note that $x^3+8=x^3+(2)^3$. Now use (1) to factor..

Quote:

2. 8x^3 + 27
Note that $8x^3+27=(2x)^3+(3)^3$. Now use (1) to factor..

Quote:

3. 64 - y^3
Note that $64-y^3=(4)^3-y^3$. Now use (2) to factor..

Quote:

4. 2u^3 +16v^3
Note that $2u^3+16v^3=(\sqrt[3]{2}u)^3+(2\sqrt[3]{2}v)^3$. Now use (1) to factor..

Quote:

5. d^6 + f^3
Note that $d^6+f^3=(d^2)^3+f^3$. Now use (1) to factor..

Quote:

6. w^6 - 1
Note that $w^6-1=(w^2)^3-1^3$. Now use (2) to factor..

Quote:

Please, show work!!! :)
Thank You so so much!!
• Aug 3rd 2009, 06:36 PM
songoku
Hi tecktonikk

You have been given the formula. All you have to do is just manipulate the questions so they satisfy the formula given.

Example :
x^3 + 8 = x^3 + 2^3 , so a = x and b = 2

I'm sure you can do the rest ^^

EDIT : Nice quote at the end, Chris :)