Question

Factor. Assume that n is a natural number.
250a^3n + 16b^3n

Answer 1

Factor a 2 out of both terms.
Then each term in the parentheses is a cubic, so you have a sum of cubes.

Answer 2

@mathwiz916 I got 2(5a+2b)(25a^2 -10ab+4b^2) but it says it's wrong

Answer 3

What happened to the n's in the exponents?

Answer 4

\(250a^{3n} + 16b^{3n} =\)

\(= 2(125a^{3n} + 8b^{3n}) =\)

\(=2[(5a^n)^3 + (2b^n)^3]\)

\(= 2 (5a^n + 2b^n)[(5a^n)^2 - 5a^n \times 2b^n + (2b^n)^2]\)

\(= 2(5a^n + 2b^n)(25a^{2n} - 10 a^nb^n + 4b^{2n} )\)

If the problem did not have the n's in the exponents, you're answer would have been correct.