Simplify -3 square root of 80x^5+x^2 square root of 20x

$- 3 \sqrt{80 x^{5}} + x^{2} \sqrt{20 x}$

Simplify each term.

Rewrite $80 x^{5}$ as ${(4 x^{2})}^{2} \cdot (5 x)$ .

Factor $16$ out of $80$ .

$- 3 \sqrt{16 (5) x^{5}} + x^{2} \sqrt{20 x}$

Rewrite $16$ as $4^{2}$ .

$- 3 \sqrt{4^{2} \cdot 5 x^{5}} + x^{2} \sqrt{20 x}$

Factor out $x^{4}$ .

$- 3 \sqrt{4^{2} \cdot 5 (x^{4} x)} + x^{2} \sqrt{20 x}$

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

$- 3 \sqrt{4^{2} \cdot 5 ({(x^{2})}^{2} x)} + x^{2} \sqrt{20 x}$

Move $5$ .

$- 3 \sqrt{4^{2} {(x^{2})}^{2} \cdot 5 x} + x^{2} \sqrt{20 x}$

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

$- 3 \sqrt{{(4 x^{2})}^{2} \cdot 5 x} + x^{2} \sqrt{20 x}$

Add parentheses.

$- 3 \sqrt{{(4 x^{2})}^{2} \cdot (5 x)} + x^{2} \sqrt{20 x}$

Pull terms out from under the radical.

$- 3 (4 x^{2} \sqrt{5 x}) + x^{2} \sqrt{20 x}$

Multiply $4$ by $- 3$ .

$- 12 (x^{2} \sqrt{5 x}) + x^{2} \sqrt{20 x}$

Rewrite $20 x$ as $2^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$- 12 x^{2} \sqrt{5 x} + x^{2} \sqrt{4 (5) x}$

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

$- 12 x^{2} \sqrt{5 x} + x^{2} \sqrt{2^{2} \cdot 5 x}$

Add parentheses.

$- 12 x^{2} \sqrt{5 x} + x^{2} \sqrt{2^{2} \cdot (5 x)}$

Pull terms out from under the radical.

$- 12 x^{2} \sqrt{5 x} + x^{2} (2 \sqrt{5 x})$

Rewrite using the commutative property of multiplication.

$- 12 x^{2} \sqrt{5 x} + 2 x^{2} \sqrt{5 x}$

Add $- 12 x^{2} \sqrt{5 x}$ and $2 x^{2} \sqrt{5 x}$ .

$- 10 x^{2} \sqrt{5 x}$