What is expand (2x-e^x)*(e^{-x}+1) ?

The solution to expand (2x-e^x)*(e^{-x}+1) is 2e^{-x}x+2x-1-e^x

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expand (2x-e^x)*(e^{-x}+1)

expand

(2 x - e^{x}) \cdot (e^{- x} + 1)

2 e^{- x} x + 2 x - 1 - e^{x}

Solution steps

(2 x - e^{x}) (e^{- x} + 1)

Apply FOIL method:

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

a = 2 x, b = - e^{x}, c = e^{- x}, d = 1

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

Apply minus-plus rules

+ (- a) = - a

= 2 e^{- x} x + 2 \cdot 1 \cdot x - e^{x} e^{- x} - 1 \cdot e^{x}

Simplify

2 e^{- x} x + 2 \cdot 1 \cdot x - e^{x} e^{- x} - 1 \cdot e^{x} : 2 e^{- x} x + 2 x - 1 - e^{x}

= 2 e^{- x} x + 2 x - 1 - e^{x}

\frac{45 a}{( x + 2.9 ) ( x + 0.14 )}

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

(m^{2} - n^{2})^{2} + 2 mn

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

(2, - 7) y (- 4, 11)

What is expand (2x-e^x)*(e^{-x}+1) ?
The solution to expand (2x-e^x)*(e^{-x}+1) is 2e^{-x}x+2x-1-e^x