Factor x^(5/2)-x^(1/2)

$x^{\frac{5}{2}} - x^{\frac{1}{2}}$

Step 1

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{5}{2}} - x^{\frac{1}{2}}$ .

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{5}{2}}$ .

$x^{\frac{1}{2}} x^{\frac{4}{2}} - x^{\frac{1}{2}}$

Factor $x^{\frac{1}{2}}$ out of $- x^{\frac{1}{2}}$ .

$x^{\frac{1}{2}} x^{\frac{4}{2}} + x^{\frac{1}{2}} \cdot - 1$

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{1}{2}} x^{\frac{4}{2}} + x^{\frac{1}{2}} \cdot - 1$ .

$x^{\frac{1}{2}} (x^{\frac{4}{2}} - 1)$

Step 2

Rewrite $x^{\frac{4}{2}}$ as ${(x^{\frac{2}{2}})}^{2}$ .

$x^{\frac{1}{2}} ({(x^{\frac{2}{2}})}^{2} - 1)$

Step 3

Rewrite $1$ as $1^{2}$ .

$x^{\frac{1}{2}} ({(x^{\frac{2}{2}})}^{2} - 1^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{\frac{2}{2}}$ and $b = 1$ .

$x^{\frac{1}{2}} ((x^{\frac{2}{2}} + 1) (x^{\frac{2}{2}} - 1))$

Step 5

Factor.

Simplify.

Divide $2$ by $2$ .

$x^{\frac{1}{2}} ((x^{1} + 1) (x^{\frac{2}{2}} - 1))$

Simplify.

$x^{\frac{1}{2}} ((x + 1) (x^{\frac{2}{2}} - 1))$

Rewrite $x^{\frac{2}{2}}$ as ${(x^{\frac{1}{2}})}^{2}$ .

$x^{\frac{1}{2}} ((x + 1) ({(x^{\frac{1}{2}})}^{2} - 1))$

Rewrite $1$ as $1^{2}$ .

$x^{\frac{1}{2}} ((x + 1) ({(x^{\frac{1}{2}})}^{2} - 1^{2}))$

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{\frac{1}{2}}$ and $b = 1$ .

$x^{\frac{1}{2}} ((x + 1) ((x^{\frac{1}{2}} + 1) (x^{\frac{1}{2}} - 1)))$

Remove unnecessary parentheses.

$x^{\frac{1}{2}} ((x + 1) (x^{\frac{1}{2}} + 1) (x^{\frac{1}{2}} - 1))$

Remove unnecessary parentheses.

$x^{\frac{1}{2}} (x + 1) (x^{\frac{1}{2}} + 1) (x^{\frac{1}{2}} - 1)$

Factor x^(5/2)-x^(1/2)

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