• Aug 3rd 2009, 05:24 PM
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)
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!!
• Aug 3rd 2009, 05:33 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 $\displaystyle x^3+8=x^3+(2)^3$. Now use (1) to factor..

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

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

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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..

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

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

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