(a+b+c)^3 - (a-b-c)^3
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(a+b+c)³ - (a-b-c)³
= (a+b+c)(a+b+c)(a+b+c) - (a-b-c)(a-b-c)(a-b-c)
= (a+b+c)²(a+b+c) - (a-b-c)²(a-b-c)
= (a²+b²+c²+2ab+2bc+2ac)(a+b+c) - (a²+b²+c²-2ab+2bc-2ac)(a-b-c)
=(a³+ab²+ac²+2a²b+2abc+2a²c+a²b+b³+bc²+2ab²+2b²c+2abc+a²c+b²c+c³+2abc+2bc²+2ac²)-(a³+ab²+ac²-2a²b+2abc-2a²c-a²b-b³-b²c+2ab²-2b²c+2abc-a²c-bc²-c³+2abc-2bc²+2ac²)
= (a³+b³+c³+3ab²+3ac²+3a²b+3bc²+3a²c+3b²c+6abc) - (a³-b³-c³+3ab²+3ac²-3a²b-3b²c-3bc²-3a²c)
= a³+b³+c³+3ab²+3ac²+3a²b+3bc²+3a²c+3b²c+6abc-a³+b³+c³-3ab²-3ac²+3a²b+3b²c+3bc²+3a²c
=2b³+2c³+6a²b+6bc²+6a²c+6b²c
=2(b³+c³+3a²b+3bc²+3a²c+3b²c)
i hope this helps......
Ninadbab:
can make it more shoter
and in simple way
there is nothing complicated
i just used the identity
i used the identity (a+b+c)²= a²+b²+c²+2ab+2bc+2ac
that is why it is longer
u can use the identity (a+b+c)³= a³+b³+c³+3(a+b)(b+c)(c+a)
then it will be shor
short
Thx
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