Question

Factorize: $(x-y{)}^3+(y-z{)}^3+(z-x{)}^3$

• A. $-3(x-y)(y-z)(z-x)$
• B. $3(x-y)(y-z)(x-z)$
• C. $3(x-y)(y-z)(z-x)$
• D. None of these

Answer 1

Answer: (C)

$3(x-y)(y-z)(z-x)$

It is a simple example of identity

if (a+b+c)=0 then $a^3+b^3+c^3=3abc$

Here $(x-y)+(y-z)+(z-x)=0$

Hence $(x-y{)}^3+(y-z{)}^3+(z-x{)}^3=3(x-y\left)\right(y-z\left)\right(z-x)$