answer this friends it's urgent
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Given LHS = (a + b)^3 + (b + c)^3 + (c + a)^3 - 3(a + b)(b + c)(c + a)
= > a^3 + b^3 + 3ab(a + b) + b^3 + c^3 + 3bc(b + c) + c^3 + a^3 + 3ac(a + c) - 3(ab + ac + b^2 + bc)(c + a)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - 3(2ac + a^2b + ac^2 + a^2c + ab^2 + b^2c + bc^2)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - (6abc + 3a^2b + 3ac^2 + 3a^2c + 3ab^2 + 3b^2c + 3bc^2)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - 6abc - 3a^2b - 3ac^2 - 3a^2c - 3ab^2 - 3b^2c - 3bc^2
= > 2a^3 + 2b^3 + 2c^3 - 6abc
= > 2(a^3 + b^3 + c^3 - 3abc).
LHS = RHS.
Hope this helps!
= > a^3 + b^3 + 3ab(a + b) + b^3 + c^3 + 3bc(b + c) + c^3 + a^3 + 3ac(a + c) - 3(ab + ac + b^2 + bc)(c + a)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - 3(2ac + a^2b + ac^2 + a^2c + ab^2 + b^2c + bc^2)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - (6abc + 3a^2b + 3ac^2 + 3a^2c + 3ab^2 + 3b^2c + 3bc^2)
= > a^3 + b^3 + 3a^2b + 3ab^2 + b^3 + c^3 + 3b^2c + 3bc^2 + c^3 + a^3 + 3a^2c + 3ac^2 - 6abc - 3a^2b - 3ac^2 - 3a^2c - 3ab^2 - 3b^2c - 3bc^2
= > 2a^3 + 2b^3 + 2c^3 - 6abc
= > 2(a^3 + b^3 + c^3 - 3abc).
LHS = RHS.
Hope this helps!
Lekhraj:
mark my answer as BRAINLIEST one
Lekhraj
im lekhraj
no sidharth answered best and it is right
Thanks Again. And please don't chat here.
so
leave it
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