Question

Factorize. (p-q)3+(q-r)3+(r-p)3​

Answer 1

If x + y + z = 0 ,   then,  

x³ + y³ + z³ = 3xyz  

Let us take

x = p - q  

y = q - r  

z = r - p  

x + y + z = p - q + q - r + r - p  

x + y + z = 0  

 

Therefore, x³ + y³ + z³ = 3xyz  

(p - q)³ + (q - r)³ + (r - p)³  

= 3(p - q)(q - r)(r - p)