What is expand (1-x)(1-e^{-t}) ?

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

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expand (1-x)(1-e^{-t})

expand

(1 - x) (1 - e^{- t})

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

Solution steps

(1 - x) (1 - e^{- t})

Apply FOIL method:

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

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

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

Apply minus-plus rules

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

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

Simplify

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

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

(sin (t) + t cos (t)) \cdot (2 cos (t) - t sin (t))

(y - 3 x^{2}) d x

\frac{\frac{4}{3}}{,} (\frac{1}{8} + \frac{1}{12} B i g) \frac{34}{( 81 + 121 )}

\frac{4 ( 13 13 - 5 5 )}{9}

π \cdot (2 x + 1)^{2}

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