1. ## 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

Thank You so so much!!

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

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

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

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

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

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

Thank You so so much!!

3. 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