Question

☺️☺️Hello !☺️☺️

I Need immediate help!!

factorise : x³(y-z)³+y³(z-x)³+z³(x-y)³

it's answer is : 3xyz(x-y)(y-z)(z-x)

◀️◀️◀️I need complete Explanation! ▶️▶️▶️

Answer 1

Given Equation is x^3(y - z)^3 + y^3(z - x)^3 + z^3(x - y)^3.

It can be written as,

= > [x(y - z)]^3 + [y(z - x)]^3 + [z(x - y)]^3.

Let a = x(y - z), b = y(z - x), c = z(x - y).

Then,

= > a + b + c

= > xy - xz + yz - yx + zx + zy

= > 0.

We know that when a + b + c = 0, then a^3 + b^3 + c^3 = 3abc

= > 3(x(y - z)y(z - x)z(x - y))

= > 3xyz(x - y)(y - z)(z - x).

Hope this helps!