Algebra Examples

$\sqrt{x y} (\sqrt{x} + \sqrt{y})$

Step 1

Apply the distributive property.

$\sqrt{x y} \sqrt{x} + \sqrt{x y} \sqrt{y}$

Step 2

Multiply $\sqrt{x y} \sqrt{x}$ .

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{x y x} + \sqrt{x y} \sqrt{y}$

Step 2.2

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

$\sqrt{x^{1} x y} + \sqrt{x y} \sqrt{y}$

Step 2.3

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

$\sqrt{x^{1} x^{1} y} + \sqrt{x y} \sqrt{y}$

Step 2.4

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

$\sqrt{x^{1 + 1} y} + \sqrt{x y} \sqrt{y}$

Step 2.5

Add $1$ and $1$ .

$\sqrt{x^{2} y} + \sqrt{x y} \sqrt{y}$

Step 3

Multiply $\sqrt{x y} \sqrt{y}$ .

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Step 3.1

Combine using the product rule for radicals.

$\sqrt{x^{2} y} + \sqrt{x y \cdot y}$

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

$\sqrt{x^{2} y} + \sqrt{x y^{1 + 1}}$

Step 3.5

Add $1$ and $1$ .

$\sqrt{x^{2} y} + \sqrt{x y^{2}}$

Step 4

Simplify each term.

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Step 4.1

Pull terms out from under the radical.

$x \sqrt{y} + \sqrt{x y^{2}}$

Step 4.2

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

$x \sqrt{y} + \sqrt{y^{2} x}$

Step 4.3

Pull terms out from under the radical.

$x \sqrt{y} + y \sqrt{x}$