Algebra Examples

$\frac{{(3 x + 6 y)}^{2}}{5 x + 10 y}$

Step 1

Simplify the numerator.

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Step 1.1

Factor $3$ out of $3 x + 6 y$ .

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Step 1.1.1

Factor $3$ out of $3 x$ .

$\frac{{(3 (x) + 6 y)}^{2}}{5 x + 10 y}$

Step 1.1.2

Factor $3$ out of $6 y$ .

$\frac{{(3 (x) + 3 (2 y))}^{2}}{5 x + 10 y}$

Step 1.1.3

Factor $3$ out of $3 (x) + 3 (2 y)$ .

$\frac{{(3 (x + 2 y))}^{2}}{5 x + 10 y}$

Step 1.2

Apply the product rule to $3 (x + 2 y)$ .

$\frac{3^{2} {(x + 2 y)}^{2}}{5 x + 10 y}$

Step 1.3

Raise $3$ to the power of $2$ .

$\frac{9 {(x + 2 y)}^{2}}{5 x + 10 y}$

Step 2

Simplify terms.

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Step 2.1

Factor $5$ out of $5 x + 10 y$ .

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Step 2.1.1

Factor $5$ out of $5 x$ .

$\frac{9 {(x + 2 y)}^{2}}{5 (x) + 10 y}$

Step 2.1.2

Factor $5$ out of $10 y$ .

$\frac{9 {(x + 2 y)}^{2}}{5 (x) + 5 (2 y)}$

Step 2.1.3

Factor $5$ out of $5 (x) + 5 (2 y)$ .

$\frac{9 {(x + 2 y)}^{2}}{5 (x + 2 y)}$

Step 2.2

Cancel the common factor of ${(x + 2 y)}^{2}$ and $x + 2 y$ .

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Step 2.2.1

Factor $x + 2 y$ out of $9 {(x + 2 y)}^{2}$ .

$\frac{(x + 2 y) (9 (x + 2 y))}{5 (x + 2 y)}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $x + 2 y$ out of $5 (x + 2 y)$ .

$\frac{(x + 2 y) (9 (x + 2 y))}{(x + 2 y) \cdot 5}$

Step 2.2.2.2

Cancel the common factor.

$\frac{(x + 2 y) (9 (x + 2 y))}{(x + 2 y) \cdot 5}$

Step 2.2.2.3

Rewrite the expression.

$\frac{9 (x + 2 y)}{5}$