Find the Product 2 square root of a(3 square root of ab-5 square root of ab)

$2 \sqrt{a} (3 \sqrt{a b} - 5 \sqrt{a b})$

Step 1

Subtract $5 \sqrt{a b}$ from $3 \sqrt{a b}$ .

$2 \sqrt{a} (- 2 \sqrt{a b})$

Step 2

Multiply $2 \sqrt{a} (- 2 \sqrt{a b})$ .

Multiply $- 2$ by $2$ .

$- 4 \sqrt{a} \sqrt{a b}$

Combine using the product rule for radicals.

$- 4 \sqrt{a b a}$

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

$- 4 \sqrt{a^{1} a b}$

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

$- 4 \sqrt{a^{1} a^{1} b}$

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

$- 4 \sqrt{a^{1 + 1} b}$

Add $1$ and $1$ .

$- 4 \sqrt{a^{2} b}$

Step 3

Pull terms out from under the radical.

$- 4 a \sqrt{b}$