What is expand (e^x-2)(e^x-3) ?

The solution to expand (e^x-2)(e^x-3) is e^{2x}-5e^x+6

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expand (e^x-2)(e^x-3)

expand

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

e^{2 x} - 5 e^{x} + 6

Solution steps

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

Apply FOIL method:

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

a = e^{x}, b = - 2, c = e^{x}, d = - 3

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

Apply minus-plus rules

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

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

Simplify

e^{x} e^{x} - 3 e^{x} - 2 e^{x} + 2 \cdot 3 : e^{2 x} - 5 e^{x} + 6

= e^{2 x} - 5 e^{x} + 6

s (s + 5) (s + \frac{1}{60})

\frac{( - x + 1 - d ) ( - x + d + 1 )}{( - 2 x + 1 - d ) ( - 2 x + d + 1 )}

\frac{3 x ^{4} + 4 x ^{2} + 8 x + 18}{x ( x ^{2} + 3 ) ^{2}}

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

f (x + arctan (e^{x} + sin (x)))

What is expand (e^x-2)(e^x-3) ?
The solution to expand (e^x-2)(e^x-3) is e^{2x}-5e^x+6