Question

Factor (x-y)^6 - (x+y)^6

Answer 1

start by factoring as the difference of two squares
\[a^2-b^2=(a+b)(a-b)\] and then factor each term as the sum and difference of two cubes

Answer 2

so step one looks like
\[((x-y)^3+(x-y)^3)((x-y)^3-(x-y)^3)\]

Answer 3

then use
\[a^3+b^3=(a+b)(a^2-ab+b^2)\]
and
\[a^3-b^3=(a-b)(a^2+ab+b^2)\]to finish up