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

The solution to expand (e^{2x}+1)(e^x-1) is e^{3x}-e^{2x}+e^x-1

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

expand

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

e^{3 x} - e^{2 x} + e^{x} - 1

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

e^{x} e^{2 x} - 1 \cdot e^{2 x} + 1 \cdot e^{x} - 1 \cdot 1 : e^{3 x} - e^{2 x} + e^{x} - 1

= e^{3 x} - e^{2 x} + e^{x} - 1

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

\frac{- 8 - 13 x}{( 4 + x ) ( 2 - 5 x )}

(- 17, - 11) y (13, 7)

(\frac{y - 1}{y + 1} + 2) (y + 5) (y + 1)

What is expand (e^{2x}+1)(e^x-1) ?
The solution to expand (e^{2x}+1)(e^x-1) is e^{3x}-e^{2x}+e^x-1