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

The solution to expand (y'(x)-2y)(2-2x) is 2y'(x)-2xy'(x)-4y+4xy

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

expand

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

2 y' (x) - 2 x y' (x) - 4 y + 4 x y

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

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

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

Multiply the numbers:

2 \cdot 2 = 4

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

ro t a c i o na l (x^{2}, 3 x z^{2}, - 2 x z)

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

\frac{n ( 3 n + 1 )}{2}

6 + 5 (m + 1 = 26)

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

What is expand (y'(x)-2y)(2-2x) ?
The solution to expand (y'(x)-2y)(2-2x) is 2y'(x)-2xy'(x)-4y+4xy