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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Apply exponent rule:

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

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

\frac{8 x + 16}{( x - 4 ) ( x + 4 )}

\frac{5 ( 3 - e ^{2 t} ) e ^{- 5 t}}{2}

9 \frac{2}{3} x - 19

\frac{( 5 x - 8 ) ^{2}}{16}

(3 x + 4 y = 7,) (6 x - 3 y = - 8)

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