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

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

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

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

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

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

1^{2} = 1

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

(81 i)^{\frac{1}{4}}

(z - \frac{1}{2})^{2}

\frac{4 ( m + 3 )}{5 ( m - 3 )}

\frac{s ^{2} + 12}{s ( s + 2 ) ( s + 3 )}

\frac{- 1}{3} (x + 12)

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