Question

Докажите тождество : 2аb×(a-b)+(a-b)*(a+b)^2+6ab(b-a)=(a-b)^3

Answer 1

2ab *(a-b)+ (a-b)(a+b)²+6ab(b-a) = (a-b)³
(a-b)*2ab  + (a-b)(a+b)² -(a-b)*6ab = (a-b)³
(a-b)(2ab +(a+b)² - 6ab) = (a-b)³
(a-b)(2ab +a²+2ab +b² -6ab) = (a-b)³
(a-b)(a²-2ab +b²)  = (a-b)³
(a-b)(a-b)² = (a-b)³
(a-b)³  ≡ (a-b)³