Algebra Examples

$\sqrt{x^{3} + x^{2}} - \sqrt{4 + 4 x}$

Step 1

Factor $x^{2}$ out of $x^{3} + x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $x^{3}$ .

$\sqrt{x^{2} x + x^{2}} - \sqrt{4 + 4 x}$

Step 1.2

Multiply by $1$ .

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

Step 1.3

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

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

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

Step 2

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

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

Step 3

Pull terms out from under the radical.

$x \sqrt{x + 1^{2}} - \sqrt{4 + 4 x}$

Step 4

One to any power is one.

$x \sqrt{x + 1} - \sqrt{4 + 4 x}$

Step 5

Factor $4$ out of $4 + 4 x$ .

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Step 5.1

Factor $4$ out of $4$ .

$x \sqrt{x + 1} - \sqrt{4 \cdot 1 + 4 x}$

Step 5.2

Factor $4$ out of $4 \cdot 1 + 4 x$ .

$x \sqrt{x + 1} - \sqrt{4 (1 + x)}$

$x \sqrt{x + 1} - \sqrt{4 (1 + x)}$

Step 6

Rewrite $4 (1 + x)$ as $2^{2} (1^{2} + x)$ .

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Step 6.1

Rewrite $4$ as $2^{2}$ .

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

Step 6.2

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

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

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

Step 7

Pull terms out from under the radical.

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

Step 8

One to any power is one.

$x \sqrt{x + 1} - (2 \sqrt{1 + x})$

Step 9

Multiply $2$ by $- 1$ .

$x \sqrt{x + 1} - 2 \sqrt{1 + x}$

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