Finite Math Examples

$3 x \sqrt{4 x^{3} y} - 5 \sqrt{x^{3} y}$

Step 1

Rewrite $4 x^{3} y$ as ${(2 x)}^{2} (x y)$ .

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Step 1.1

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

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

Step 1.2

Factor out $x^{2}$ .

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

Step 1.3

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

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

Step 1.4

Add parentheses.

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1

Move $x$ .

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

Step 3.2

Multiply $x$ by $x$ .

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

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

Step 4

Multiply $2$ by $3$ .

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

Step 5

Rewrite $x^{3} y$ as $x^{2} (x y)$ .

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Step 5.1

Factor out $x^{2}$ .

$6 x^{2} \sqrt{x y} - 5 \sqrt{x^{2} x y}$

Step 5.2

Add parentheses.

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

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

Step 6

Pull terms out from under the radical.

$6 x^{2} \sqrt{x y} - 5 x \sqrt{x y}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$