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

The solution to (2+sqrt(1-x^2))^2 is -x^2+4sqrt(1-x^2)+5

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

simplify

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

- x^{2} + 4 1 - x^{2} + 5

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

2^{2} + 2 \cdot 2 1 - x^{2} + (1 - x^{2})^{2} : - x^{2} + 4 1 - x^{2} + 5

= - x^{2} + 4 1 - x^{2} + 5

π (1 + x^{2})^{2}

\frac{( n + 1 ) ^{2}}{4 n}

\frac{( n ^{2} - 3 n - 2 ) ^{2}}{4}

\frac{n ( 3 n + 5 )}{3}

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

What is (2+sqrt(1-x^2))^2 ?
The solution to (2+sqrt(1-x^2))^2 is -x^2+4sqrt(1-x^2)+5