SOLUTION: (It don't have in textbook but teacher gives me worksheet) Can you help me solve this problem: June factored the polynomial c^9-d^12 into (c^3+d^4)(c^6-c^3*d^4+d^8). Is sh

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Question 167092: (It don't have in textbook but teacher gives me worksheet)
Can you help me solve this problem:
June factored the polynomial c^9-d^12 into (c^3+d^4)(c^6-c^3*d^4+d^8).
Is she correct? How do u know?
MANY THANKS
Found 2 solutions by checkley77, Earlsdon:
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
She is correct.
Proof:
c^6-c^3*d^4+d^8
c^3+d^4 multiply
----------------------------
c^9-c^6d^4+c^3d^8+c^6d^4-c^3d^8+d^12
c^9+d^12 answer.

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
June is not correct!
How do we know?
One way to prove this is to multiply the two factors, using FOIL, to see if you arrive at the given polynomial.
Simplifying.
and this is not the same as the given polynomial of
Another way is to recognize the given polynomial as the difference of two cubes:
and the difference of two cubes is factored thus:
where: and
and this is not what June got!