What is expand (x((dy)/(dx))+y)^2 ?

The solution to expand (x((dy)/(dx))+y)^2 is x^2(dy)/(dx)^2+2xy(dy)/(dx)+y^2

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expand (x((dy)/(dx))+y)^2

expand

(x (\frac{d y}{d x}) + y)^{2}

x^{2} \frac{d y}{d x}^{2} + 2 x y \frac{d y}{d x} + y^{2}

Solution steps

(x (\frac{d y}{d x}) + y)^{2}

Remove parentheses:

(a) = a

= (x \frac{d y}{d x} + y)^{2}

Apply Perfect Square Formula:

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

a = x \frac{d y}{d x}, b = y

= (x \frac{d y}{d x})^{2} + 2 x \frac{d y}{d x} y + y^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= x^{2} \frac{d y}{d x}^{2} + 2 x y \frac{d y}{d x} + y^{2}

\frac{( s + 3 )}{( s + 1 ) ^{2}}

\frac{π ( 17 17 - 1 )}{96}

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

m + 6 m - 6

(1, 3) (- 2, x - 2)

What is expand (x((dy)/(dx))+y)^2 ?
The solution to expand (x((dy)/(dx))+y)^2 is x^2(dy)/(dx)^2+2xy(dy)/(dx)+y^2