SOLUTION: I just took a math test and wanted to see if I had done this right. 10. Factor 512y^3-729 I determined that each side of this expression was a cube. 8^3=512, 9^3=729.

Question 350620: I just took a math test and wanted to see if I had done this right.
10. Factor
512y^3-729
I determined that each side of this expression was a cube. 8^3=512, 9^3=729. So I answered: (8y x 8y x 8y)-(9 x 9 x 9). Was this correct?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Hate to be a bearer of bad news but you didn't get it right.
.
512y^3-729
can be rewritten (as you say) as:
(8y)^3-9^3
At this point you have a "difference of cubes" -- a special case for factoring:
a^3 � b^3 = (a � b)(a^2 + ab + b^2)
.
which then gives you:
(8y - 9)((8y)^2 + (8y)(9) + 9^2)
(8y - 9)(64y^2 + 72y + 81)

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