Simplify
\[ (x^2+y^2-z^2)^2-(x^2-y^2+z^2)^2 \]
Solution:
Using identity:
\[ a^2-b^2=(a-b)(a+b) \]
\[ = \left[(x^2+y^2-z^2)-(x^2-y^2+z^2)\right] \left[(x^2+y^2-z^2)+(x^2-y^2+z^2)\right] \]
\[ = (2y^2-2z^2)(2x^2) \]
\[ = 4x^2(y^2-z^2) \]
\[ (x^2+y^2-z^2)^2-(x^2-y^2+z^2)^2 \]
Using identity:
\[ a^2-b^2=(a-b)(a+b) \]
\[ = \left[(x^2+y^2-z^2)-(x^2-y^2+z^2)\right] \left[(x^2+y^2-z^2)+(x^2-y^2+z^2)\right] \]
\[ = (2y^2-2z^2)(2x^2) \]
\[ = 4x^2(y^2-z^2) \]