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

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

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

factor

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

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

Solution steps

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

Simplify

4 x^{2} y^{2} : (2 x y)^{2}

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

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

Simplify

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

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

35 x^{3} + 20 x^{2} - 175 x - 100

0.9 \cdot 2

3 x - 4 < 3 x - 5

∣ y ∣ < 6

4 t - 3 < - 11 or 3 t + 5 > 14

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