verify that x³-y³-z³-3xyz = ½(x-y-z) [(x-y)²-(3-z)²-(z-y)²] . . plz ans. this wid explanaition Question verify that x³-y³-z³-3xyz = ½(x-y-z) [(x-y)²-(3-z)²-(z-y)²]..plz ans. this wid explanaition in progress 0 Math Rylee 6 months 2021-12-10T17:05:12+00:00 2021-12-10T17:05:12+00:00 1 Answer 0 views 0

## Answers ( )

Answer:

First the formula is

x^3+y^3+z^3-3xyz= (x+y+z) (x^2+y^2+z^2-xy-yz-zx)

We need to prove the above equation is equal to this formula

Solving RHS

it is in the form (a-b)^2= a^2+b^2-2ab

=1/2 (x+y+z) (x-y)^2-(3-z)^2-(z-y)^2

=1/2 (x+y+z) [(x^2+y^2-2xy) (y^2+z^2-2yz) (z^2+x^2-2zx)]

=1/2 (x+y+z) [(2x^2+y^2+2z^2-2xy-2yz-2zx)]

In this u can see 2 is common lets take it outside

=1/2 (x+y+z) 2[x^2+y^2+z^2-xy-yz-zx]

In this 1/2 gets cancelled with the common 2

=(x-y-z) [x^2+y^2+z^2-xy-yz-zx]

Hence, it is appropriate with the formula

x^3+y^3+z^3-3xyz.

It is equal to =LHS

Hence proved

THANK YOU

I HOPE IT HELPS