Question

Упростите выражение:
$sqrt{ {x}^{3} - {y}^{3} + {x}^{2} times y - {y}^{2} times x }$
где x>y>0
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Answer 1

$sqrt{x^3-y^3+x^2y-y^2x}=sqrt{(x^3-y^2x)+(x^2y-y^3)}=\\sqrt{x(x^2-y^2)+y(x^2-y^2)}=sqrt{(x^2-y^2)(x+y)}=\\sqrt{(x-y)(x+y)(x+y)}=sqrt{(x-y)(x+y)^2}=|x+y|sqrt{x-y}=(x+y)sqrt{x-y}$