# Verify that x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2] - Mathematics

Verify that x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]

#### Solution

It is known that,

x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)

therefore x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]

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

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

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

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#### APPEARS IN

NCERT Class 9 Mathematics Textbook
Chapter 2 Polynomials
Exercise 2.5 | Q 12 | Page 49