Algebra Examples

$x \sqrt{50 x} - 3 \sqrt{32 x^{3}}$

Step 1

Rewrite $50 x$ as $5^{2} \cdot (2 x)$ .

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Step 1.1

Factor $25$ out of $50$ .

$x \sqrt{25 (2) x} - 3 \sqrt{32 x^{3}}$

Step 1.2

Rewrite $25$ as $5^{2}$ .

$x \sqrt{5^{2} \cdot 2 x} - 3 \sqrt{32 x^{3}}$

Step 1.3

Add parentheses.

$x \sqrt{5^{2} \cdot (2 x)} - 3 \sqrt{32 x^{3}}$

Step 2

Pull terms out from under the radical.

$x (| 5 | \sqrt{2 x}) - 3 \sqrt{32 x^{3}}$

Step 3

Rewrite using the commutative property of multiplication.

$| 5 | x \sqrt{2 x} - 3 \sqrt{32 x^{3}}$

Step 4

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$5 x \sqrt{2 x} - 3 \sqrt{32 x^{3}}$

Step 5

Rewrite $32 x^{3}$ as ${(4 x)}^{2} \cdot (2 x)$ .

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Step 5.1

Factor $16$ out of $32$ .

$5 x \sqrt{2 x} - 3 \sqrt{16 (2) x^{3}}$

Step 5.2

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

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

Step 5.3

Factor out $x^{2}$ .

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

Step 5.4

Move $2$ .

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

Step 5.5

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

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

Step 5.6

Add parentheses.

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

Step 6

Pull terms out from under the radical.

$5 x \sqrt{2 x} - 3 (| 4 x | \sqrt{2 x})$

Step 7

Remove non-negative terms from the absolute value.

$5 x \sqrt{2 x} - 3 (4 | x | \sqrt{2 x})$

Step 8

Multiply $4$ by $- 3$ .

$5 x \sqrt{2 x} - 12 | x | \sqrt{2 x}$