SOLUTION: Factor. 64+27w^3

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Question 1116140: Factor.
64+27w^3
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
64%2B27w%5E3
%282%5E3%29%5E2%2B3%5E3w%5E3
%282%5E2%29%5E3%2B%283w%29%5E3
4%5E3%2B%283w%29%5E3
A special factorization rule can be derived (or looked for in a reference source) for sum of cubes.

%284%2B3w%29%284%5E2-4%2A3w%2B%283w%29%5E2%29

%284%2B3w%29%2816-12w%2B9w%5E2%29

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
There is canonical algebraic decomposition (identity)


a%5E3+%2B+b%5E3 = %28a%2Bb%29%2A%28a%5E2-+ab%2Bb%5E2%29.


Use it. In your case a = 4  (and a%5E3 = 64);  b = 3w  (and b%5E3= 27w%5E3 ).


Therefore,  64+%2B+27w%5E3 = %284%2B3w%29%2A%2816+-+12w+%2B+9w%5E2%29.

See the lessons
    - The sum of cubes formula
in this site.