Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Multiply $\sqrt{2 x} \sqrt{2}$ .

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Step 1.2.1

Combine using the product rule for radicals.

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

Step 1.2.2

Multiply $2$ by $2$ .

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

Step 1.3

Rewrite using the commutative property of multiplication.

$\sqrt{4 x} - \sqrt{2 x} \sqrt{x} - 5 \sqrt{x}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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

Step 1.4.2

Pull terms out from under the radical.

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

Step 1.4.3

Multiply $- \sqrt{2 x} \sqrt{x}$ .

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Step 1.4.3.1

Combine using the product rule for radicals.

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

Step 1.4.3.2

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

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

Step 1.4.3.3

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

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

Step 1.4.3.4

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

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

Step 1.4.3.5

Add $1$ and $1$ .

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

Step 1.4.4

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

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

Step 1.4.5

Pull terms out from under the radical.

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

Step 2

Subtract $5 \sqrt{x}$ from $2 \sqrt{x}$ .

$- x \sqrt{2} - 3 \sqrt{x}$