Q: Use suitable identity to find the following product.

(Question from Polynomials chapter, question is attached below in the image (PNG)

Experts Please help...........)

Asked by prakash.sanyasi | 28th Dec, 2019, 04:59: AM

Expert Answer:

(x+y+z)(x²+y²+z²-xy-yz-zx)=x³+y³+z³-3xyz.....(1)
Now,
(a-b-c)(a²+b²+c²+ab-bc+ca)
=[a+(-b)+(-c)][a²+(-b)²+(-c)²-a(-b)-(-b)(-c)-(-c)a]
= a³+(-b)³+(-c)³-3a(-b)(-c)
= a³-b³-c³-3abc.......From (1)
Therefore,
(a-b-c)(a²+b²+c²+ab-bc+ca)=a³-b³-c³-3abc

Answered by Arun | 28th Dec, 2019, 08:44: AM