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

The solution to expand (x+4yy'(x))^2 is x^2+8xyy'(x)+16y^2(y'(x))^2

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expand (x+4yy'(x))^2

expand

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

x^{2} + 8 x yy' (x) + 16 y^{2} (y' (x))^{2}

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Simplify

x^{2} + 2 x \cdot 4 y y^{'} (x) + (4 y y^{'} (x))^{2} : x^{2} + 8 x y y^{'} (x) + 16 y^{2} (y^{'} (x))^{2}

= x^{2} + 8 x y y^{'} (x) + 16 y^{2} (y^{'} (x))^{2}

(x^{2} - 3 x + 2)^{6}

48 (\frac{7}{3} - ln (3))

\frac{s - 1}{s ( s - 3 ) ( s + 3 )}

(t - 1) H (t - 1)

\frac{18 - 12 x}{( 4 x - 1 ) ( x - 4 )}

What is expand (x+4yy'(x))^2 ?
The solution to expand (x+4yy'(x))^2 is x^2+8xyy'(x)+16y^2(y'(x))^2