What is expand (e^t+1)(e^t-k) ?

The solution to expand (e^t+1)(e^t-k) is e^{2t}-ke^t+e^t-k

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expand (e^t+1)(e^t-k)

expand

(e^{t} + 1) (e^{t} - k)

e^{2 t} - k e^{t} + e^{t} - k

Solution steps

(e^{t} + 1) (e^{t} - k)

Apply FOIL method:

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

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

e^{t} e^{t} - k e^{t} + 1 \cdot e^{t} - 1 \cdot k : e^{2 t} - k e^{t} + e^{t} - k

= e^{2 t} - k e^{t} + e^{t} - k

3 (- 2 e^{- 2 x} + 3 x^{2} - 2 x - 3)

3 sin (2 (x - \frac{π}{4}))

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

(A e^{- k x} + A e^{k x})^{2}

1 - x^{2} + (π - arccos (x)) x

What is expand (e^t+1)(e^t-k) ?
The solution to expand (e^t+1)(e^t-k) is e^{2t}-ke^t+e^t-k