Question 47089
{{{(x^(2n) + 2x^n * y^n + y^(2n)) * (x^(2n) - 2x^n * y^n + y^(2n))}}}
note that {{{x^(2n) = (x^n)^2}}}
and {{{y^(2n) = (y^n)^2}}}
now say {{{w = x^n }}} and {{{z = y^n }}}
now
{{{(w^2 + 2wz + z^2) * (w^2 - 2wz + z^2)}}}
multiplying out, I get
{{{ w^4 + z^4 - 2w^2 * z^2}}}
now transform back
{{{w = x^n }}}
{{{z = y^n }}}
{{{x^(4n) + z^(4n) - 2x^(2n)* y^(2n) }}} answer
you can do a check by saying
n = 1
x = 2
y = 3
then
{{{(x^(2n) + 2x^n * y^n + y^(2n)) * (x^(2n) - 2x^n * y^n + y^(2n))}}}
{{{(4 + 12 + 9)* (4 - 12 + 9) = 25}}}
{{{25 = 25}}}
{{{x^(4n) + z^(4n) - 2x^(2n)* y^(2n) }}}
{{{16 + 81 - 72 = 25}}}
{{{25 = 25}}}
checks OK