Question

(x+y+z)whole square+(x-y+z)whole square+(x+y-z) whole square​

Answer 1

(x+y+z)² + (x+y+z)² + (x+y+z)²

(identity to use : (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ac )

by using this identity,

(x+y+z)² + (x+y+z)² + (x+y+z)²

=  (x² + y² + z² + 2(x)(z) + 2(y)(z) + 2(x)(y) ) + (x² + y² + z² + 2(x)(z) + 2(y)(z) + 2(x)(y) ) + (x² + y² + z² + 2(x)(z) + 2(y)(z) + 2(x)(y) )

= (x² + y² + z² + 2xz + 2yz + 2xy) + (x² + y² + z² + 2xz + 2yz + 2xy) + (x² + y² + z² + 2xz + 2yz + 2xy)

= x² + y² + z² + 2xz + 2yz + 2xy + x² + y² + z² + 2xz + 2yz + 2xy + x² +  y² + z² + 2xz + 2yz + 2xy

= x²+ x²+ x² + y² + y² + y² + z² + z² + z² + 2xz + 2xz + 2xz + 2yz + 2yz + 2yz + 2xy + 2xy + 2xy

= 3x² + 3y² + 3z² + 6xz + 6yz + 6xy

= 3(x² + y² + z²) + 6(xz + yz + xy)

Hope it helps!

have a great day!