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Popular >

expand e^x(e^x+1)^2

Solution

expand

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

Solution

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

Solution steps

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

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

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

Distribute parentheses

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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