What is expand (y'(x)-1)(y+2x) ?

The solution to expand (y'(x)-1)(y+2x) is y'(x)y+2xy'(x)-y-2x

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expand (y'(x)-1)(y+2x)

expand

(y^{'} (x) - 1) (y + 2 x)

y' (x) y + 2 x y' (x) - y - 2 x

Solution steps

(y^{'} (x) - 1) (y + 2 x)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = y^{'} (x), b = - 1, c = y, d = 2 x

= y^{^{'}} (x) y + y^{^{'}} (x) 2 x + (- 1) y + (- 1) \cdot 2 x

Apply minus-plus rules

+ (- a) = - a

= y^{^{'}} (x) y + 2 x y^{^{'}} (x) - 1 \cdot y - 1 \cdot 2 x

Simplify

y^{'} (x) y + 2 x y^{'} (x) - 1 \cdot y - 1 \cdot 2 x : y^{'} (x) y + 2 x y^{'} (x) - y - 2 x

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

\frac{1}{6} (2 x^{\frac{3}{2}} - 2 - sin (2 (x^{\frac{3}{2}} - 1))) + C

(x^{3} - 2 x) l e f t (5 x^{2} + 2)

\frac{d y}{( y - m ) ( y - n )}

What is expand (y'(x)-1)(y+2x) ?
The solution to expand (y'(x)-1)(y+2x) is y'(x)y+2xy'(x)-y-2x