Algebra Examples

$\frac{3 a}{b^{2}} \cdot \frac{a b + b^{2}}{9}$

Step 1

Factor $b$ out of $a b + b^{2}$ .

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Step 1.1

Factor $b$ out of $a b$ .

$\frac{3 a}{b^{2}} \cdot \frac{b a + b^{2}}{9}$

Step 1.2

Factor $b$ out of $b^{2}$ .

$\frac{3 a}{b^{2}} \cdot \frac{b a + b \cdot b}{9}$

Step 1.3

Factor $b$ out of $b a + b \cdot b$ .

$\frac{3 a}{b^{2}} \cdot \frac{b (a + b)}{9}$

$\frac{3 a}{b^{2}} \cdot \frac{b (a + b)}{9}$

Step 2

Combine.

$\frac{3 a (b (a + b))}{b^{2} \cdot 9}$

Step 3

Cancel the common factor of $3$ and $9$ .

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Step 3.1

Factor $3$ out of $3 a (b (a + b))$ .

$\frac{3 (a (b (a + b)))}{b^{2} \cdot 9}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $b^{2} \cdot 9$ .

$\frac{3 (a (b (a + b)))}{3 (b^{2} \cdot 3)}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (a (b (a + b)))}{3 (b^{2} \cdot 3)}$

Step 3.2.3

Rewrite the expression.

$\frac{a (b (a + b))}{b^{2} \cdot 3}$

$\frac{a (b (a + b))}{b^{2} \cdot 3}$

$\frac{a (b (a + b))}{b^{2} \cdot 3}$

Step 4

Cancel the common factor of $b$ and $b^{2}$ .

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Step 4.1

Factor $b$ out of $a (b (a + b))$ .

$\frac{b (a (a + b))}{b^{2} \cdot 3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b$ out of $b^{2} \cdot 3$ .

$\frac{b (a (a + b))}{b (b \cdot 3)}$

Step 4.2.2

Cancel the common factor.

$\frac{b (a (a + b))}{b (b \cdot 3)}$

Step 4.2.3

Rewrite the expression.

$\frac{a (a + b)}{b \cdot 3}$

$\frac{a (a + b)}{b \cdot 3}$

$\frac{a (a + b)}{b \cdot 3}$

Step 5

Move $3$ to the left of $b$ .

$\frac{a (a + b)}{3 b}$

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