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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

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

Simplify

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

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

\frac{1}{( t + 1 ) ^{4}}

(3 + 4 t^{4} + 2 e^{- 4 t}) u (t)

y^{2} (e^{2 x} + c)

(x - 6) (x +!)

1 - sin^{2} (x) (1 - tan^{2} (x) = 1)

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