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Prove that (a+b+c)^3 -a^3-b^3-c^3 =3(a+b) (b+c) …

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Prove that (a+b+c)^3 -a^3-b^3-c^3 =3(a+b) (b+c) (c+a)

Posted by Chinmayee Kumari Sahu 2 years, 3 months ago

CBSE > Class 09 > Mathematics

1 answers

Aanvi Saxena 2 years, 3 months ago

=>(a+b+c) 3 =(a 3 +3a 2 b+3ab 2 +b 3 )+3(a 2 +2ab+b 2 )c+3(a+b)c 2 +c 3 =>(a+b+c) 3 =a 3 +b 3 +c 3 +3a 2 b+3a 2 c+3ab 2 +3b 2 c+3ac 2 +3bc 2 +6abc =>(a+b+c) 3 =a 3 +b 3 +c 3 +3a 2 b+3a 2 c+3ab 2 +3b 2 c+3ac 2 +3bc 2 +3abc+3abc =>(a+b+c) 3 =a 3 +b 3 +c 3 +3a(ab+ac+b 2 +bc)+3c(ab+ac+b 2 +bc) =>(a+b+c) 3 =a 3 +b 3 +c 3 +3(a+c)(ab+ac+b 2 +bc) =>(a+b+c) 3 =a 3 +b 3 +c 3 +3(a+c)[a(b+c)+b(b+c)] =>(a+b+c) 3 =a 3 +b 3 +c 3 +3(a+c)(b+c)(a+b) =>(a+b+c) 3 −a 3 −b 3 −c 3 =3(a+c)(b+c)(a+b)

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