Question

Solve ${\left(x+y\right)}^4-{\left(x-y\right)}^4$

Answer 1

${(x+y)}^4-{(x-y)}^4={\left\{{(x+y)}^2\right\}}^2-{\left\{{(x-y)}^2\right\}}^2=$$\{{(x+y)}^2+{(x-y)}^2\}\{{(x+y)}^2-{(x-y)}^2\}$$=\{x^2+2xy+y^2+x^2-2xy+y^2\}\left[\{(x+y)+(x-y)\}\{(x+y)-(x-y)\}\right]$

$=2(x^2+y^2)\times 2x\times 2y=8xy(x^2+y^2)$