Algebra Examples

$- 5 x^{2} \sqrt{6 x^{3}} + x \sqrt{96 x^{5}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $6 x^{3}$ as $x^{2} \cdot (6 x)$ .

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Step 1.1.1

Factor out $x^{2}$ .

$- 5 x^{2} \sqrt{6 (x^{2} x)} + x \sqrt{96 x^{5}}$

Step 1.1.2

Reorder $6$ and $x^{2}$ .

$- 5 x^{2} \sqrt{x^{2} \cdot 6 x} + x \sqrt{96 x^{5}}$

Step 1.1.3

Add parentheses.

$- 5 x^{2} \sqrt{x^{2} \cdot (6 x)} + x \sqrt{96 x^{5}}$

Step 1.2

Pull terms out from under the radical.

$- 5 x^{2} (x \sqrt{6 x}) + x \sqrt{96 x^{5}}$

Step 1.3

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 1.3.1

Move $x$ .

$- 5 (x \cdot x^{2}) \sqrt{6 x} + x \sqrt{96 x^{5}}$

Step 1.3.2

Multiply $x$ by $x^{2}$ .

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Step 1.3.2.1

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

$- 5 (x^{1} x^{2}) \sqrt{6 x} + x \sqrt{96 x^{5}}$

Step 1.3.2.2

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

$- 5 x^{1 + 2} \sqrt{6 x} + x \sqrt{96 x^{5}}$

Step 1.3.3

Add $1$ and $2$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{96 x^{5}}$

Step 1.4

Rewrite $96 x^{5}$ as ${(4 x^{2})}^{2} \cdot (6 x)$ .

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Step 1.4.1

Factor $16$ out of $96$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{16 (6) x^{5}}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{4^{2} \cdot 6 x^{5}}$

Step 1.4.3

Factor out $x^{4}$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{4^{2} \cdot 6 (x^{4} x)}$

Step 1.4.4

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{4^{2} \cdot 6 ({(x^{2})}^{2} x)}$

Step 1.4.5

Move $6$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{4^{2} {(x^{2})}^{2} \cdot 6 x}$

Step 1.4.6

Rewrite $4^{2} {(x^{2})}^{2}$ as ${(4 x^{2})}^{2}$ .

$- 5 x^{3} \sqrt{6 x} + x \sqrt{{(4 x^{2})}^{2} \cdot 6 x}$

Step 1.4.7

Add parentheses.

$- 5 x^{3} \sqrt{6 x} + x \sqrt{{(4 x^{2})}^{2} \cdot (6 x)}$

Step 1.5

Pull terms out from under the radical.

$- 5 x^{3} \sqrt{6 x} + x (4 x^{2} \sqrt{6 x})$

Step 1.6

Rewrite using the commutative property of multiplication.

$- 5 x^{3} \sqrt{6 x} + 4 x (x^{2} \sqrt{6 x})$

Step 1.7

Multiply $x$ by $x^{2}$ by adding the exponents.

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Step 1.7.1

Move $x^{2}$ .

$- 5 x^{3} \sqrt{6 x} + 4 (x^{2} x) \sqrt{6 x}$

Step 1.7.2

Multiply $x^{2}$ by $x$ .

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Step 1.7.2.1

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

$- 5 x^{3} \sqrt{6 x} + 4 (x^{2} x^{1}) \sqrt{6 x}$

Step 1.7.2.2

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

$- 5 x^{3} \sqrt{6 x} + 4 x^{2 + 1} \sqrt{6 x}$

Step 1.7.3

Add $2$ and $1$ .

$- 5 x^{3} \sqrt{6 x} + 4 x^{3} \sqrt{6 x}$

Step 2

Add $- 5 x^{3} \sqrt{6 x}$ and $4 x^{3} \sqrt{6 x}$ .

$- x^{3} \sqrt{6 x}$