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Popular >

factor e^{2x}+2e^x+1

Solution

factor

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

Solution

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

Solution steps

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

Apply exponent rule:

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

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

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

Rewrite

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

as

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

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = e^{x}, b = 1

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

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Frequently Asked Questions (FAQ)

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