Factorize #x^2+y^2+z^2-xy-yz-zx?#

Question

#x^2+y^2+z^2-xy-yz-zx#

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Answer 1 · 2018-01-02T00:37:03

See below.

Making

#m = x-y#
#n = y-z#
#p = x-z#

we have

#m^2+n^2+p^2 = 2(x^2+y^2+z^2-x*y-x*z-y*z)#

then

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