What is (sqrt(x^2+y^2+1)-4)^2 ?

The solution to (sqrt(x^2+y^2+1)-4)^2 is x^2+y^2-8sqrt(x^2+y^2+1)+17

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simplify (sqrt(x^2+y^2+1)-4)^2

simplify

(x^{2} + y^{2} + 1 - 4)^{2}

x^{2} + y^{2} - 8 x^{2} + y^{2} + 1 + 17

Solution steps

(x^{2} + y^{2} + 1 - 4)^{2}

Apply Perfect Square Formula:

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

(x^{2} + y^{2} + 1 - 4)^{2} = (x^{2} + y^{2} + 1)^{2} - 2 x^{2} + y^{2} + 1 \cdot 4 + 4^{2}

= (x^{2} + y^{2} + 1)^{2} - 2 x^{2} + y^{2} + 1 \cdot 4 + 4^{2}

Simplify

(x^{2} + y^{2} + 1)^{2} - 2 x^{2} + y^{2} + 1 \cdot 4 + 4^{2} : x^{2} + y^{2} - 8 x^{2} + y^{2} + 1 + 17

= x^{2} + y^{2} - 8 x^{2} + y^{2} + 1 + 17

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\frac{( 2 x - 3 ) ( x + 9 )}{4 x ( 2 x - 9 )}

\frac{- 2 s ^{2} - 1}{( s ^{2} + 1 ) ^{2}}

What is (sqrt(x^2+y^2+1)-4)^2 ?
The solution to (sqrt(x^2+y^2+1)-4)^2 is x^2+y^2-8sqrt(x^2+y^2+1)+17