Question

Correct answer will definitely be brainliest and the person will be followed. Answer question no. 26

Answer 1

Given Equation is in the form of a^3 + b^3 + c^3 - 3abc where a = x+y, b = y+z, c = z+x.

We know that a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)  -- (1)

On substituting the values in (1), we get

= (x+y+y+z+z+x)((x+y)^2 + (y+z)^2 + (z+x)^2 - (x+y)(y+z) - (y+z)(z+x) - (z+x)(x+y)


We know that (a +b)^2 = a^2 + b^2 + 2ab.


= 2(x+y+z)(x^2+y^2+2xy + y^2+z^2+2yz + z^2+x^2+2zx - xy - xz -y^2 - yz - yz  - yx - z^2 - zx - zx - zy - x^2 - xy)


= 2(x+y+z)(x^2+y^2+z^2+2xy+2yz+2zx-3xy-3zx-3yz-2y^2-2z^2-2x^2)


= 2(x+y+z)(x^2 + y^2 + z^2 - xy - yz - zx)


= 2(x^3 + y^3 + z^3 - 3xyz).


Hope this helps!