Algebra Examples

$e^{2 x} - e^{x}$

Step 1

Rewrite $e^{2 x}$ as ${(e^{x})}^{2}$ .

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

Step 2

Let $u = e^{x}$ . Substitute $u$ for all occurrences of $e^{x}$ .

$u^{2} - u$

Step 3

Factor $u$ out of $u^{2} - u$ .

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Step 3.1

Factor $u$ out of $u^{2}$ .

$u \cdot u - u$

Step 3.2

Factor $u$ out of $- u$ .

$u \cdot u + u \cdot - 1$

Step 3.3

Factor $u$ out of $u \cdot u + u \cdot - 1$ .

$u (u - 1)$

Step 4

Replace all occurrences of $u$ with $e^{x}$ .

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