CBSE Class 9 Answered
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 | 28 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
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 | 28 Dec, 2019, 08:44: AM
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