Algebra Examples

$4 x^{\frac{3}{2}} (x^{3} + x^{2}) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$

Step 1

Factor $2 x^{\frac{3}{2}}$ out of $4 x^{\frac{3}{2}} (x^{3} + x^{2}) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$ .

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Step 1.1

Factor $2 x^{\frac{3}{2}}$ out of $4 x^{\frac{3}{2}} (x^{3} + x^{2})$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) - 6 x^{\frac{5}{2}} - 6 x^{\frac{3}{2}}$

Step 1.2

Factor $2 x^{\frac{3}{2}}$ out of $- 6 x^{\frac{5}{2}}$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) + 2 x^{\frac{3}{2}} (- 3 x^{\frac{2}{2}}) - 6 x^{\frac{3}{2}}$

Step 1.3

Factor $2 x^{\frac{3}{2}}$ out of $- 6 x^{\frac{3}{2}}$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) + 2 x^{\frac{3}{2}} (- 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$

Step 1.4

Factor $2 x^{\frac{3}{2}}$ out of $2 x^{\frac{3}{2}} (2 (x^{3} + x^{2})) + 2 x^{\frac{3}{2}} (- 3 x^{\frac{2}{2}})$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$

Step 1.5

Factor $2 x^{\frac{3}{2}}$ out of $2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}}) + 2 x^{\frac{3}{2}} (- 3)$ .

$2 x^{\frac{3}{2}} (2 (x^{3} + x^{2}) - 3 x^{\frac{2}{2}} - 3)$

Step 2

Apply the distributive property.

$2 x^{\frac{3}{2}} (2 x^{3} + 2 x^{2} - 3 x^{\frac{2}{2}} - 3)$

Step 3

Divide $2$ by $2$ .

$2 x^{\frac{3}{2}} (2 x^{3} + 2 x^{2} - 3 x^{1} - 3)$

Step 4

Simplify.

$2 x^{\frac{3}{2}} (2 x^{3} + 2 x^{2} - 3 x - 3)$

Step 5

Factor.

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Step 5.1

Rewrite $2 x^{3} + 2 x^{2} - 3 x - 3$ in a factored form.

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Step 5.1.1

Factor out the greatest common factor from each group.

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Step 5.1.1.1

Group the first two terms and the last two terms.

$2 x^{\frac{3}{2}} ((2 x^{3} + 2 x^{2}) - 3 x - 3)$

Step 5.1.1.2

Factor out the greatest common factor (GCF) from each group.

$2 x^{\frac{3}{2}} (2 x^{2} (x + 1) - 3 (x + 1))$

Step 5.1.2

Factor the polynomial by factoring out the greatest common factor, $x + 1$ .

$2 x^{\frac{3}{2}} ((x + 1) (2 x^{2} - 3))$

Step 5.2

Remove unnecessary parentheses.

$2 x^{\frac{3}{2}} (x + 1) (2 x^{2} - 3)$