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prove that (a+b+c)3 - a3- b3 - c3 = 3(a+b) (b+c) (c+a).

Posted by Shivang Bhatia 5 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 5 years, 1 month ago

(a+b+c)³ - a³-b³-c³ = [(a+b)+c]³ – a³-b³-c³

= (a+b)³+c³+3c(a+b)(a+b+c)-a³-b³-c³

= a³+b³+3ab(a+b)+c³+3c(a+b)(a+b+c)-a³-b³-c³

= a³+b³+c³+3ab(a+b)+3c(a+b)(a+b+c)-a³-b³-c³

= 3ab(a+b)+3c(a+b)(a+b+c) 3(a+b)[ab+c(a+b+c)]

= 3(a+b)[ab+ac+bc+c²] 3(a+b)[a(b+c)+c(b+c)]

= 3(a+b)(b+c)(c+a)

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Posted by T Prudhvi 2 weeks, 4 days ago

CBSE > Class 09 > Mathematics