What is factor e^{4x}-1 ?

The solution to factor e^{4x}-1 is (e^{2x}+1)(e^x+1)(e^x-1)

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factor e^{4x}-1

factor

e^{4 x} - 1

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

Solution steps

e^{4 x} - 1

Apply exponent rule:

a^{b c} = (a^{b})^{c}

e^{4 x} = (e^{x})^{4}

= (e^{x})^{4} - 1

Rewrite

(e^{x})^{4} - 1

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

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

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

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

Factor

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

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

Simplify

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

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

(2 x - 1)^{2} - 5 (2 x - 1) + 6

x^{6} + 5 x

3 a c + 3 a d + 2 b c + 2 b d

- 169 y^{6} + 100 m^{2} n^{4}

l {e^{- 3 t}}

What is factor e^{4x}-1 ?
The solution to factor e^{4x}-1 is (e^{2x}+1)(e^x+1)(e^x-1)