Question

разложите на множители х^4+х^2у^2+у^4

Answer 1

$x^4+x^2y^2+y^4=(x^4+2x^2y^2+y^4)-x^2y^2=\\\\=\underbrace {(x^2+y^2)^2-(xy)^2}_{A^2-B^2}=(x^2+y^2-xy)\cdot (x^2+y^2+xy)\\\\\\A^2-B^2=(A-B)(A+B)$