What is expand (e^x-1)(e^x+3) ?

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

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expand (e^x-1)(e^x+3)

expand

(e^{x} - 1) (e^{x} + 3)

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

Solution steps

(e^{x} - 1) (e^{x} + 3)

Apply FOIL method:

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

a = e^{x}, b = - 1, c = e^{x}, d = 3

= e^{x} e^{x} + e^{x} \cdot 3 + (- 1) e^{x} + (- 1) \cdot 3

Apply minus-plus rules

+ (- a) = - a

= e^{x} e^{x} + 3 e^{x} - 1 \cdot e^{x} - 1 \cdot 3

Simplify

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

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

\frac{( x ^{5} - 2 ) ( x - 2 )}{x ^{6}}

\frac{x ( x - 16 ) ( x - 24 ) ( x - 32 ) ( x - 40 )}{786432}

(4.4 x - 3.3) ln (4.7 x + 6.6)

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

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

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