What is (8-sqrt((x-2)^2+y^2))^2 ?

The solution to (8-sqrt((x-2)^2+y^2))^2 is x^2-4x+y^2-16sqrt((x-2)^2+y^2)+68

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simplify (8-sqrt((x-2)^2+y^2))^2

simplify

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

x^{2} - 4 x + y^{2} - 16 (x - 2)^{2} + y^{2} + 68

Solution steps

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

Apply Perfect Square Formula:

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

(8 - (x - 2)^{2} + y^{2})^{2} = 8^{2} - 2 \cdot 8 (x - 2)^{2} + y^{2} + ((x - 2)^{2} + y^{2})^{2}

= 8^{2} - 2 \cdot 8 (x - 2)^{2} + y^{2} + ((x - 2)^{2} + y^{2})^{2}

Simplify

8^{2} - 2 \cdot 8 (x - 2)^{2} + y^{2} + ((x - 2)^{2} + y^{2})^{2} : x^{2} - 4 x + y^{2} - 16 (x - 2)^{2} + y^{2} + 68

= x^{2} - 4 x + y^{2} - 16 (x - 2)^{2} + y^{2} + 68

+ (2 x + 3 y) d y

\frac{( x - 2 ) ( x - 5 )}{( x - 3 ) ^{2}}

\frac{120 ( - x ^{2} + 4 )}{( x ^{2} + x + 4 ) ^{2}}

\frac{sin ( b ) - cot ( b ) ( 1 + cos ( b ) )}{1 + cos ( b )}

3 x^{\frac{1}{3}} (2 x - 1)

What is (8-sqrt((x-2)^2+y^2))^2 ?
The solution to (8-sqrt((x-2)^2+y^2))^2 is x^2-4x+y^2-16sqrt((x-2)^2+y^2)+68