Question

Докажите тождество
4а^2б^2(а^2+б^2)-(а^2+б^2)^3=(б^2-а^2)(а^4-б^4)

Answer 1

4a²б²(а²+б²)-(а²+б²)³=(а²+б²)(4а²б²-(а²+б²)²=
=(а²+б²)(-(а⁴+2а²б²+б⁴-4а²б²))=-(а²+б²)(а⁴-2а²б²+б⁴)=
=-(а²+б²)(а²-б²)²=-(а²+б²)(а²-б²)(а²-б²)=-(а²-б²)(а⁴-б⁴)≡(б²-а²)(а⁴-б⁴).