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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

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

- 2^{- 2} + 4

4^{2} + (- 2^{2}) + 5

\frac{( x + 4 ) ( x + 6 )}{40}

\frac{2 ( 30 + 1155 )}{5}

\frac{s}{2 ( s ^{2} + ( 2 a + 2 k ) ^{2} )}

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