SOLUTION: PLease help to factor 64a^3c^6 - 27x^9

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Question 67302This question is from textbook An Incremenatl Development
: PLease help to factor
64a^3c^6 - 27x^9This question is from textbook An Incremenatl Development

Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
You should recognise this as the dference of two cubes:
64%5E3c%5E6+-+27x%5E9+=+%284ac%5E2%29%5E3+-+%283x%5E3%29%5E3
The difference of two cubes can be factored as follows:
A%5E3+-+B%5E3+=+%28A-B%29%28A%5E2%2B2AB%2BB%5E2%29
In this problem; A+=+4ac%5E2 and B+=+3x%5E3 Applying the factor.
%284ac%5E2%29+-+%283x%5E3%29+=+%284ac%5E2+-+3x%5E3%29%28%284ac%5E2%29%5E2+%2B+2%284ac%5E2%29%283x%5E3%29+%2B+%283x%5E3%29%5E2%29 Simplifying:
%284ac%5E2+-+3x%5E3%29%2816a%5E2c%5E4+%2B+24ac%5E2x%5E3+%2B+9x%5E6%29