What is (x^2+y^2-z^2)^2-4x^2y^2 ?

The solution to (x^2+y^2-z^2)^2-4x^2y^2 is x^4+y^4+z^4-3x^2y^2-x^2z^2+y^2x^2-y^2z^2-z^2x^2-z^2y^2

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simplify (x^2+y^2-z^2)^2-4x^2y^2

simplify

(x^{2} + y^{2} - z^{2})^{2} - 4 x^{2} y^{2}

x^{4} + y^{4} + z^{4} - 3 x^{2} y^{2} - x^{2} z^{2} + y^{2} x^{2} - y^{2} z^{2} - z^{2} x^{2} - z^{2} y^{2}

Solution steps

(x^{2} + y^{2} - z^{2})^{2} - 4 x^{2} y^{2}

Expand

(x^{2} + y^{2} - z^{2})^{2} : x^{4} + x^{2} y^{2} - x^{2} z^{2} + y^{2} x^{2} + y^{4} - y^{2} z^{2} - z^{2} x^{2} - z^{2} y^{2} + z^{4}

= x^{4} + x^{2} y^{2} - x^{2} z^{2} + y^{2} x^{2} + y^{4} - y^{2} z^{2} - z^{2} x^{2} - z^{2} y^{2} + z^{4} - 4 x^{2} y^{2}

Group like terms

= x^{4} + y^{4} + z^{4} + x^{2} y^{2} - 4 x^{2} y^{2} - x^{2} z^{2} + y^{2} x^{2} - y^{2} z^{2} - z^{2} x^{2} - z^{2} y^{2}

Add similar elements:

x^{2} y^{2} - 4 x^{2} y^{2} = - 3 x^{2} y^{2}

= x^{4} + y^{4} + z^{4} - 3 x^{2} y^{2} - x^{2} z^{2} + y^{2} x^{2} - y^{2} z^{2} - z^{2} x^{2} - z^{2} y^{2}

\frac{( x - 1 )}{( x ^{3} - 1 )}

(2 x^{2} \cdot y)^{4}

- 4 a \cdot (a^{- 1} \cdot b^{2})^{3}

(54 y^{19} z^{3})^{\frac{1}{3}}

\frac{3}{x} + \frac{2}{x}

What is (x^2+y^2-z^2)^2-4x^2y^2 ?
The solution to (x^2+y^2-z^2)^2-4x^2y^2 is x^4+y^4+z^4-3x^2y^2-x^2z^2+y^2x^2-y^2z^2-z^2x^2-z^2y^2