Simplify 7x square root of 125x^2-7x^2 square root of 5

$7 x \sqrt{125 x^{2}} - 7 x^{2} \sqrt{5}$

Simplify each term.

Rewrite $125 x^{2}$ as ${(5 x)}^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$7 x \sqrt{25 (5) x^{2}} - 7 x^{2} \sqrt{5}$

Rewrite $25$ as $5^{2}$ .

$7 x \sqrt{5^{2} \cdot 5 x^{2}} - 7 x^{2} \sqrt{5}$

Move $5$ .

$7 x \sqrt{5^{2} x^{2} \cdot 5} - 7 x^{2} \sqrt{5}$

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

$7 x \sqrt{{(5 x)}^{2} \cdot 5} - 7 x^{2} \sqrt{5}$

Pull terms out from under the radical.

$7 x (5 x \sqrt{5}) - 7 x^{2} \sqrt{5}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$7 (x \cdot x) (5 \sqrt{5}) - 7 x^{2} \sqrt{5}$

Multiply $x$ by $x$ .

$7 x^{2} (5 \sqrt{5}) - 7 x^{2} \sqrt{5}$

Multiply $5$ by $7$ .

$35 x^{2} \sqrt{5} - 7 x^{2} \sqrt{5}$

Subtract $7 x^{2} \sqrt{5}$ from $35 x^{2} \sqrt{5}$ .

$28 x^{2} \sqrt{5}$