Question

show that (x+y+z)^3 - (x+y-z)^3 - (y+z-x)^3 - (z+x-y)^3 = 24xyz

please help me to do this​

Answer 1

Here given that,

(x+y+z)^3 - (x+y-z)^3 - (y+z-x)^3 - (z+x-y)^3

(x+y+z)^3+(x−y−z)^3−(x−y+z)^3−(x+y−z)^3

=((x+y+z)^3−(x+y−z)^3)+((x−y−z)^3−(x−y+z)^3)

=2z(3(x+y)2+z2)−2z(3(x−y)2+z2)

=2z(3⋅4xy)

=24xy

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We use,

(x+y+z)3−(x+y−z)3=2z((x+y+z)2+(x+y−z)2)+(x+y)2−z2)=2z(3(x+y)2+z2)

and,

and,(x−y−z)3−(x−y+z)3=−2z((x−y−z)2+(x−y+z)2)+(x−y)2−z2)=2z(3(x−y)2+z2)

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Answer 2

Answer:(x+y+z)^3 -(x+y-z^3)-(y+z-x)^3-(2+x-y)^3=24xy

Step-by-step explanation: