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

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

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expand (cos(x)-e^{-x})(-cos(x)-e^{-x})

expand

(cos (x) - e^{- x}) (- cos (x) - e^{- x})

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

Solution steps

(cos (x) - e^{- x}) (- cos (x) - e^{- x})

Apply FOIL method:

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

a = cos (x), b = - e^{- x}, c = - cos (x), d = - e^{- x}

= cos (x) (- cos (x)) + cos (x) (- e^{- x}) + (- e^{- x}) (- cos (x)) + (- e^{- x}) (- e^{- x})

Apply minus-plus rules

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

= - cos (x) cos (x) - e^{- x} cos (x) + e^{- x} cos (x) + e^{- x} e^{- x}

Simplify

- cos (x) cos (x) - e^{- x} cos (x) + e^{- x} cos (x) + e^{- x} e^{- x} : - cos^{2} (x) + e^{- 2 x}

= - cos^{2} (x) + e^{- 2 x}

- (2 cos (x) + 1) (2 cos (x) - 1) sin^{2} (x)

\frac{1}{s \cdot ( s + 2 )}

(12 b^{20} - 9 m^{\frac{3}{2}})^{2}

\frac{s ^{2} + 1}{( s ^{2} + s + 10 ) s ^{2}}

t (x) x^{^{''}} + (5 t (x) - 5) x^{^{'}} + 5 x

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