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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

20

1 + \frac{1.6 K ( x + 2 ) ( T x + 1 )}{x ^{2} + 2 x + 1.64}

\frac{10 ( s ^{2} + 119 )}{( s + 5 ) ( s ^{2} + 10 s + 169 )}

\frac{1}{9} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

\frac{10}{s ( s + 4 )}

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