Simplify square root of x^3+x^2- square root of 4+4x

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

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

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

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

Multiply by $1$ .

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

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

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

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

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

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

Pull terms out from under the radical.

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

One to any power is one.

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

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

Factor $4$ out of $4$ .

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

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

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

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

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

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

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

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

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

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

Pull terms out from under the radical.

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

One to any power is one.

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

Multiply $2$ by $- 1$ .

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

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