Algebra Examples

$\sqrt{7 x} (\sqrt{x} - 7 \sqrt{7})$

Step 1

Apply the distributive property.

$\sqrt{7 x} \sqrt{x} + \sqrt{7 x} (- 7 \sqrt{7})$

Step 2

Multiply $\sqrt{7 x} \sqrt{x}$ .

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Step 2.1

Combine using the product rule for radicals.

$\sqrt{7 x \cdot x} + \sqrt{7 x} (- 7 \sqrt{7})$

Step 2.2

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

$\sqrt{7 (x^{1} x)} + \sqrt{7 x} (- 7 \sqrt{7})$

Step 2.3

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

$\sqrt{7 (x^{1} x^{1})} + \sqrt{7 x} (- 7 \sqrt{7})$

Step 2.4

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

$\sqrt{7 x^{1 + 1}} + \sqrt{7 x} (- 7 \sqrt{7})$

Step 2.5

Add $1$ and $1$ .

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

Step 3

Multiply $\sqrt{7 x} (- 7 \sqrt{7})$ .

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Step 3.1

Combine using the product rule for radicals.

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

Step 3.2

Multiply $7$ by $7$ .

$\sqrt{7 x^{2}} - 7 \sqrt{49 x}$

Step 4

Simplify each term.

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Step 4.1

Reorder $7$ and $x^{2}$ .

$\sqrt{x^{2} \cdot 7} - 7 \sqrt{49 x}$

Step 4.2

Pull terms out from under the radical.

$x \sqrt{7} - 7 \sqrt{49 x}$

Step 4.3

Rewrite $49$ as $7^{2}$ .

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

Step 4.4

Pull terms out from under the radical.

$x \sqrt{7} - 7 (7 \sqrt{x})$

Step 4.5

Multiply $7$ by $- 7$ .

$x \sqrt{7} - 49 \sqrt{x}$