What is (sqrt(1-x^2-y^2)+1)^2 ?

The solution to (sqrt(1-x^2-y^2)+1)^2 is -x^2-y^2+2sqrt(1-x^2-y^2)+2

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simplify (sqrt(1-x^2-y^2)+1)^2

simplify

(1 - x^{2} - y^{2} + 1)^{2}

- x^{2} - y^{2} + 2 1 - x^{2} - y^{2} + 2

Solution steps

(1 - x^{2} - y^{2} + 1)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(1 - x^{2} - y^{2} + 1)^{2} = (1 - x^{2} - y^{2})^{2} + 2 1 - x^{2} - y^{2} \cdot 1 + 1^{2}

= (1 - x^{2} - y^{2})^{2} + 2 1 - x^{2} - y^{2} \cdot 1 + 1^{2}

Simplify

(1 - x^{2} - y^{2})^{2} + 2 1 - x^{2} - y^{2} \cdot 1 + 1^{2} : - x^{2} - y^{2} + 2 1 - x^{2} - y^{2} + 2

= - x^{2} - y^{2} + 2 1 - x^{2} - y^{2} + 2

(z^{2} - \frac{3}{z})^{8}

- (2 + i - t i)^{2} i

\frac{( 2 x + 1 ) 3 x}{2}

(2 e^{x} - 2 e^{- x})^{3}

e^{t x} \cdot (e^{t} - 1)

What is (sqrt(1-x^2-y^2)+1)^2 ?
The solution to (sqrt(1-x^2-y^2)+1)^2 is -x^2-y^2+2sqrt(1-x^2-y^2)+2