Algebra Examples

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

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

Step 1

Rewrite

e^{2 x}

$e^{2 x}$ as

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

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

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

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

Step 2

Let

u = e^{x}

$u = e^{x}$ . Substitute

u

$u$ for all occurrences of

e^{x}

$e^{x}$ .

u^{2} - u

$u^{2} - u$

Step 3

Factor

u

$u$ out of

u^{2} - u

$u^{2} - u$ .

Tap for more steps...

Step 3.1

Factor

u

$u$ out of

u^{2}

$u^{2}$ .

u \cdot u - u

$u \cdot u - u$

Step 3.2

Factor

u

$u$ out of

- u

$- u$ .

u \cdot u + u \cdot - 1

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

Step 3.3

Factor

u

$u$ out of

u \cdot u + u \cdot - 1

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

u (u - 1)

$u (u - 1)$

u (u - 1)

$u (u - 1)$

Step 4

Replace all occurrences of

u

$u$ with

e^{x}

$e^{x}$ .

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

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

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$