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Ilyasssssss
@Ilyasssssss
August 2022
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[tex] (a+b+c)^{3} - a^{3} -b^{3} -c^{3} [/tex]
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MizoriesKun
(a+b+c)³-a³-b³-c³= ((a+b+c)³-a³) - (b³+c³) =
=(a+b+c- a)*((a+b+c)²+(a+b+c)*a+a²) - (b+c)(b²-bc+c²) =
= (b+c)*(((a+b+c)²+(a+b+c)*a+a²)- (b²-bc+c²) =
= (b+c)*(a²+b²+c²+2ab+2ac+2bc +a²+ab+ac+a² - b²+bc-c²) =
=(b+c)*(3a²+3ab+3ac+3bc ) =3*(b+c)*(a²+ab+ac+bc) =
= 3*(b+c)*(a*(a+b+c)+bc)
2 votes
Thanks 3
Ilyasssssss
https://znanija.com/task/24907540
Ilyasssssss
https://znanija.com/task/24907548
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Answers & Comments
=(a+b+c- a)*((a+b+c)²+(a+b+c)*a+a²) - (b+c)(b²-bc+c²) =
= (b+c)*(((a+b+c)²+(a+b+c)*a+a²)- (b²-bc+c²) =
= (b+c)*(a²+b²+c²+2ab+2ac+2bc +a²+ab+ac+a² - b²+bc-c²) =
=(b+c)*(3a²+3ab+3ac+3bc ) =3*(b+c)*(a²+ab+ac+bc) =
= 3*(b+c)*(a*(a+b+c)+bc)