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Squidwardo
@Squidwardo
July 2022
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Разложите на множители выражение (a+b)(a-2b)^2-(a-b)^3-2b^3
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nafanya2014
Verified answer
(a+b)(a-2b)²-(a-b)³-2b³==(a+b)(a-2b)²-((a-b)³+2b³)=[ во второй скобке формула суммы кубов]=
=(a+b)(a-2b)²-((a-b)+2b)((a-b)²-(a-b)·2b + (2b)²)=
=(a+b)(a-2b)²- ( a-b+2b) ( (a-b)²-(a-b)·2b + (2b)²)=
=(a+b)( (a-2b)²- (a-b)²+(a-b)·2b-(2b)²)=
=(a+b) ( a²-4ab+4b²-a²+2ab-b²+2ab-2b²-4b²)=
=(a+b)(-3b²)= -3b²(a+b)
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Answers & Comments
Verified answer
(a+b)(a-2b)²-(a-b)³-2b³==(a+b)(a-2b)²-((a-b)³+2b³)=[ во второй скобке формула суммы кубов]==(a+b)(a-2b)²-((a-b)+2b)((a-b)²-(a-b)·2b + (2b)²)=
=(a+b)(a-2b)²- ( a-b+2b) ( (a-b)²-(a-b)·2b + (2b)²)=
=(a+b)( (a-2b)²- (a-b)²+(a-b)·2b-(2b)²)=
=(a+b) ( a²-4ab+4b²-a²+2ab-b²+2ab-2b²-4b²)=
=(a+b)(-3b²)= -3b²(a+b)