Question

(x+y-z)^2+(x-y+z)^2​

Answer 1

Step-by-step explanation:

x²+y²-z²+x²-y²+z²

x^4-y^4-z^4. is the answer thanx.

Answer 2

Using The Method Of Expansions:

(x+y-z)^2 + (x-y+z)^2

= x^2 + y^2 + z^2 +2( xy-yz-xz) + x^2 + y^2 + z^2 +2(xz-xy-yz)

= x^2 + y^2 + z^2 + 2xy -2yz -2xz + x^2 + y^2 + z^2 +2xz - 2xy - 2yz

2xy, -2xz - 2yz + 2xz - 2xy -2yz will all cancel with each other....

= x^2 + y^2 + z^2 + x^2 + y^2 + z^2

= 2 x^2 + 2y^2 + 2z^2

= 2 (x^2 + y^2 + z^2) which is your final answer.

Hope it helps you.

Happy learning.