What is expand (0.5e^x+0.5)(0.5e^{-x}+0.5) ?

The solution to expand (0.5e^x+0.5)(0.5e^{-x}+0.5) is 0.25e^x+0.25e^{-x}+0.5

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expand (0.5e^x+0.5)(0.5e^{-x}+0.5)

expand

(0.5 e^{x} + 0.5) (0.5 e^{- x} + 0.5)

0.25 e^{x} + 0.25 e^{- x} + 0.5

Solution steps

(0.5 e^{x} + 0.5) (0.5 e^{- x} + 0.5)

Apply FOIL method:

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

a = 0.5 e^{x}, b = 0.5, c = 0.5 e^{- x}, d = 0.5

= 0.5 e^{x} \cdot 0.5 e^{- x} + 0.5 e^{x} \cdot 0.5 + 0.5 \cdot 0.5 e^{- x} + 0.5 \cdot 0.5

= 0.5 \cdot 0.5 e^{x} e^{- x} + 0.5 \cdot 0.5 e^{x} + 0.5 \cdot 0.5 e^{- x} + 0.5 \cdot 0.5

Simplify

0.5 \cdot 0.5 e^{x} e^{- x} + 0.5 \cdot 0.5 e^{x} + 0.5 \cdot 0.5 e^{- x} + 0.5 \cdot 0.5 : 0.25 e^{x} + 0.25 e^{- x} + 0.5

= 0.25 e^{x} + 0.25 e^{- x} + 0.5

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

2 (- sin (a) cos (3 a) - 3 cos (a) sin (3 a)) + sin (2 a)

\frac{x ^{2}}{( x ^{2} + 1 ) ( 1 + y ^{2} )}

\frac{1}{3} ((3 + \frac{y}{6})^{2} - 3^{2}) y

(x^{\frac{1}{3}} + y^{\frac{1}{3}})^{3}

What is expand (0.5e^x+0.5)(0.5e^{-x}+0.5) ?
The solution to expand (0.5e^x+0.5)(0.5e^{-x}+0.5) is 0.25e^x+0.25e^{-x}+0.5