What are symmetric expression & how is it used for factorisation of polynomials?

Asked by araima2001 | 13th May, 2014, 11:06: AM

Expert Answer:

Symmetric expression is an expression, if it is invariant under any permutations of its variables,
That is, if you change the position of the variables, the value of the expression is unaltered.
Consider the expression x cubed plus y cubed :
Here, different permutations are: f open parentheses x comma y close parentheses space a n d space f open parentheses y comma x close parentheses:
Thus, the values are: x cubed plus y cubed space a n d space y cubed plus x cubed
It is clear that the values are invariant.
Now to check the factorization of x cubed plus y cubed :
W e space k n o w space t h a t comma x cubed plus y cubed equals open parentheses x plus y close parentheses open parentheses x squared minus x y plus y squared close parentheses
Hence the factorization of x cubed plus y cubed equals open parentheses x plus y close parentheses open parentheses x squared minus x y plus y squared close parentheses

Answered by Vimala Ramamurthy | 15th May, 2014, 12:07: PM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.