Simplify -4x^2 square root of 5x^2-x^3 square root of 180

$- 4 x^{2} \sqrt{5 x^{2}} - x^{3} \sqrt{180}$

Simplify each term.

Reorder $5$ and $x^{2}$ .

$- 4 x^{2} \sqrt{x^{2} \cdot 5} - x^{3} \sqrt{180}$

Pull terms out from under the radical.

$- 4 x^{2} (x \sqrt{5}) - x^{3} \sqrt{180}$

Multiply $x^{2}$ by $x$ by adding the exponents.

Move $x$ .

$- 4 (x \cdot x^{2}) \sqrt{5} - x^{3} \sqrt{180}$

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$- 4 (x^{1} x^{2}) \sqrt{5} - x^{3} \sqrt{180}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 4 x^{1 + 2} \sqrt{5} - x^{3} \sqrt{180}$

Add $1$ and $2$ .

$- 4 x^{3} \sqrt{5} - x^{3} \sqrt{180}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$- 4 x^{3} \sqrt{5} - x^{3} \sqrt{36 (5)}$

Rewrite $36$ as $6^{2}$ .

$- 4 x^{3} \sqrt{5} - x^{3} \sqrt{6^{2} \cdot 5}$

Pull terms out from under the radical.

$- 4 x^{3} \sqrt{5} - x^{3} (6 \sqrt{5})$

Multiply $6$ by $- 1$ .

$- 4 x^{3} \sqrt{5} - 6 x^{3} \sqrt{5}$

Subtract $6 x^{3} \sqrt{5}$ from $- 4 x^{3} \sqrt{5}$ .

$- 10 x^{3} \sqrt{5}$