What is expand (x/(4y'(x))+y)^2 ?

The solution to expand (x/(4y'(x))+y)^2 is (x^2)/(16(y'(x))^2)+(xy)/(2y'(x))+y^2

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expand (x/(4y'(x))+y)^2

expand

(\frac{x}{4 y ^{'} ( x )} + y)^{2}

\frac{x ^{2}}{16 ( y ' ( x ) ) ^{2}} + \frac{x y}{2 y ' ( x )} + y^{2}

Solution steps

(\frac{x}{4 y ^{'} ( x )} + y)^{2}

Apply Perfect Square Formula:

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

a = \frac{x}{4 y ^{'} ( x )}, b = y

= (\frac{x}{4 y ^{^{'}} ( x )})^{2} + 2 \cdot \frac{x}{4 y ^{^{'}} ( x )} y + y^{2}

Simplify

(\frac{x}{4 y ^{'} ( x )})^{2} + 2 \cdot \frac{x}{4 y ^{'} ( x )} y + y^{2} : \frac{x ^{2}}{16 ( y ^{'} ( x ) ) ^{2}} + \frac{x y}{2 y ^{'} ( x )} + y^{2}

= \frac{x ^{2}}{16 ( y ^{'} ( x ) ) ^{2}} + \frac{x y}{2 y ^{'} ( x )} + y^{2}

p u n t os (2, - 1) y (\frac{1 , - 9}{7})

\frac{1}{90} (e^{8 x} + 8 e^{8 x} x)

(e^{i θ} + e^{- i θ})^{2}

\frac{x + 2}{2 ( x - 1 )}

x (2 x - 1) e^{x}

What is expand (x/(4y'(x))+y)^2 ?
The solution to expand (x/(4y'(x))+y)^2 is (x^2)/(16(y'(x))^2)+(xy)/(2y'(x))+y^2