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

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

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

expand

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

Apply exponent rule:

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

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

- \frac{2 ( x - y )}{a}

(1 + c e^{t})^{2}

(2 + 6 x) x^{2} e^{x}

\frac{120 ( N - 2 )}{N}

(sec^{2} (π x) - 1)^{3}

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