What is (4sqrt(5)-sqrt(x^2-4x+y^2+2y+5))^2 ?

The solution to (4sqrt(5)-sqrt(x^2-4x+y^2+2y+5))^2 is x^2-4x+y^2+2y-8sqrt(5)sqrt(x^2-4x+y^2+2y+5)+85

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simplify (4sqrt(5)-sqrt(x^2-4x+y^2+2y+5))^2

simplify

(45 - x^{2} - 4 x + y^{2} + 2 y + 5)^{2}

x^{2} - 4 x + y^{2} + 2 y - 85 x^{2} - 4 x + y^{2} + 2 y + 5 + 85

Solution steps

(45 - x^{2} - 4 x + y^{2} + 2 y + 5)^{2}

Apply Perfect Square Formula:

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

(45 - x^{2} - 4 x + y^{2} + 2 y + 5)^{2} = (45)^{2} - 2 \cdot 45 x^{2} - 4 x + y^{2} + 2 y + 5 + (x^{2} - 4 x + y^{2} + 2 y + 5)^{2}

= (45)^{2} - 2 \cdot 45 x^{2} - 4 x + y^{2} + 2 y + 5 + (x^{2} - 4 x + y^{2} + 2 y + 5)^{2}

Simplify

(45)^{2} - 2 \cdot 45 x^{2} - 4 x + y^{2} + 2 y + 5 + (x^{2} - 4 x + y^{2} + 2 y + 5)^{2} : x^{2} - 4 x + y^{2} + 2 y - 85 x^{2} - 4 x + y^{2} + 2 y + 5 + 85

= x^{2} - 4 x + y^{2} + 2 y - 85 x^{2} - 4 x + y^{2} + 2 y + 5 + 85

(3 x + \frac{4.5}{x})^{8}

(900 - 0.01 x ln (x)) \cdot 400

\frac{25 ( e ^{\frac{4}{5}} - 1 )}{2 e ^{\frac{2}{5}}}

\frac{( 5 x ^{3} + 3 x y + 2 y ^{2} )}{x ( x + 2 )}

(x^{2} + 1) (y^{3} - 2)

What is (4sqrt(5)-sqrt(x^2-4x+y^2+2y+5))^2 ?
The solution to (4sqrt(5)-sqrt(x^2-4x+y^2+2y+5))^2 is x^2-4x+y^2+2y-8sqrt(5)sqrt(x^2-4x+y^2+2y+5)+85