What is expand ((x^2+y^2)^{1/2}+3y)^2 ?

The solution to expand ((x^2+y^2)^{1/2}+3y)^2 is x^2+10y^2+6y(x^2+y^2)^{1/2}

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expand ((x^2+y^2)^{1/2}+3y)^2

expand

((x^{2} + y^{2})^{\frac{1}{2}} + 3 y)^{2}

x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}

Solution steps

((x^{2} + y^{2})^{\frac{1}{2}} + 3 y)^{2}

Apply Perfect Square Formula:

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

((x^{2} + y^{2})^{\frac{1}{2}} + 3 y)^{2} = ((x^{2} + y^{2})^{\frac{1}{2}})^{2} + 2 (x^{2} + y^{2})^{\frac{1}{2}} \cdot 3 y + (3 y)^{2}

= ((x^{2} + y^{2})^{\frac{1}{2}})^{2} + 2 (x^{2} + y^{2})^{\frac{1}{2}} \cdot 3 y + (3 y)^{2}

Simplify

((x^{2} + y^{2})^{\frac{1}{2}})^{2} + 2 (x^{2} + y^{2})^{\frac{1}{2}} \cdot 3 y + (3 y)^{2} : x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}

= x^{2} + 10 y^{2} + 6 y (x^{2} + y^{2})^{\frac{1}{2}}

(4 x^{2} + 3 cos (y)) d x - x sin (y) d y

- 10 x^{\frac{2}{3}} (4 x^{4} - 4 x^{2} + 5)

\frac{( x ^{2} - b ) \cdot y \cdot tan ( 7 )}{cos ( x ^{2} ) \cdot π r}

\frac{16 a ^{2} + 12 ab + 9 b ^{3}}{2 ( 16 a ^{2} + 12 ab + 9 b ^{2} )}

(2 + 5) x + y

What is expand ((x^2+y^2)^{1/2}+3y)^2 ?
The solution to expand ((x^2+y^2)^{1/2}+3y)^2 is x^2+10y^2+6y(x^2+y^2)^{1/2}