IIT JEE , AIEEE Forum - Mathematics , Algebra

nadeemoidu

1)
Here's a good method of factorizing.
Take the given expression as f(a) = a ( b^2 c^2 - a^2 ) + b ( c^2 + a^2 - b^2 ) + c ( a^2 + b^2 - c^2 ) - 2 abc

Find f [ -(b+c) ] . Here it is equal to 0.

So ( a - b - c ) is a factor of the given expression.

By the symmetry in a,b,c , we can see that ( - a + b - c) and ( - a - b + c) are also factors.

So the final answer should be ( -a + b +c ) ( a - b + c )( a + b - c)

In general if u get f( b) =0 , then (a-b) is a factor. if f( -b) =0 then ( a+b) is a factor and so on.

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