What is expand (xy'(x)-y)^2 ?

The solution to expand (xy'(x)-y)^2 is x^2(y'(x))^2-2xy'(x)y+y^2

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expand (xy'(x)-y)^2

expand

(x y^{'} (x) - y)^{2}

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

Solution steps

(x y^{'} (x) - y)^{2}

Apply Perfect Square Formula:

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

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

= (x y^{^{'}} (x))^{2} - 2 x y^{^{'}} (x) y + y^{2}

Apply exponent rule:

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

= x^{2} (y^{^{'}} (x))^{2} - 2 x y^{^{'}} (x) y + y^{2}

2 a (\frac{1}{5} b + \frac{t}{2})

\frac{( 2 + 5 y ) ^{2}}{4}

(x + 1.5) \cdot (x + 0, 3) \cdot (x - 2, 7)

(1 - 22)^{4}

\frac{d x}{( x ^{2} + 1 ) ^{2}}

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