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askaelizade145
@askaelizade145
July 2022
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Докажите тождество : 2аb×(a-b)+(a-b)*(a+b)^2+6ab(b-a)=(a-b)^3
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zhenyaM2002
Verified answer
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
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Answers & Comments
Verified answer
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