Factor x^(3/2)-x^(1/2)

$x^{\frac{3}{2}} - x^{\frac{1}{2}}$

Step 1

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{3}{2}} - x^{\frac{1}{2}}$ .

Factor $x^{\frac{1}{2}}$ out of $x^{\frac{3}{2}}$ .

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

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

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

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

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

Step 2

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

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

Step 3

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

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

Step 4

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 $b = 1$ .

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

Remove unnecessary parentheses.

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

Factor x^(3/2)-x^(1/2)

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