Basic Math Examples

$\frac{16 a^{2} - 4 a}{a + 1} \cdot \frac{3 a^{2} + 9 a + 6}{16 a^{2} - 4 a}$

Step 1

Factor $4 a$ out of $16 a^{2} - 4 a$ .

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Step 1.1

Factor $4 a$ out of $16 a^{2}$ .

$\frac{4 a (4 a) - 4 a}{a + 1} \cdot \frac{3 a^{2} + 9 a + 6}{16 a^{2} - 4 a}$

Step 1.2

Factor $4 a$ out of $- 4 a$ .

$\frac{4 a (4 a) + 4 a (- 1)}{a + 1} \cdot \frac{3 a^{2} + 9 a + 6}{16 a^{2} - 4 a}$

Step 1.3

Factor $4 a$ out of $4 a (4 a) + 4 a (- 1)$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 a^{2} + 9 a + 6}{16 a^{2} - 4 a}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $3$ out of $3 a^{2} + 9 a + 6$ .

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Step 2.1.1

Factor $3$ out of $3 a^{2}$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a^{2}) + 9 a + 6}{16 a^{2} - 4 a}$

Step 2.1.2

Factor $3$ out of $9 a$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a^{2}) + 3 (3 a) + 6}{16 a^{2} - 4 a}$

Step 2.1.3

Factor $3$ out of $6$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 a^{2} + 3 (3 a) + 3 \cdot 2}{16 a^{2} - 4 a}$

Step 2.1.4

Factor $3$ out of $3 a^{2} + 3 (3 a)$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a^{2} + 3 a) + 3 \cdot 2}{16 a^{2} - 4 a}$

Step 2.1.5

Factor $3$ out of $3 (a^{2} + 3 a) + 3 \cdot 2$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a^{2} + 3 a + 2)}{16 a^{2} - 4 a}$

Step 2.2

Factor $a^{2} + 3 a + 2$ using the AC method.

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Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $2$ and whose sum is $3$ .

$1, 2$

Step 2.2.2

Write the factored form using these integers.

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 ((a + 1) (a + 2))}{16 a^{2} - 4 a}$

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a + 1) (a + 2)}{16 a^{2} - 4 a}$

Step 3

Simplify terms.

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Step 3.1

Factor $4 a$ out of $16 a^{2} - 4 a$ .

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Step 3.1.1

Factor $4 a$ out of $16 a^{2}$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a + 1) (a + 2)}{4 a (4 a) - 4 a}$

Step 3.1.2

Factor $4 a$ out of $- 4 a$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a + 1) (a + 2)}{4 a (4 a) + 4 a (- 1)}$

Step 3.1.3

Factor $4 a$ out of $4 a (4 a) + 4 a (- 1)$ .

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a + 1) (a + 2)}{4 a (4 a - 1)}$

Step 3.2

Cancel the common factor of $4 a (4 a - 1)$ .

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Step 3.2.1

Cancel the common factor.

$\frac{4 a (4 a - 1)}{a + 1} \cdot \frac{3 (a + 1) (a + 2)}{4 a (4 a - 1)}$

Step 3.2.2

Rewrite the expression.

$\frac{1}{a + 1} \cdot (3 (a + 1) (a + 2))$

Step 3.3

Cancel the common factor of $a + 1$ .

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Step 3.3.1

Factor $a + 1$ out of $3 (a + 1) (a + 2)$ .

$\frac{1}{a + 1} \cdot ((a + 1) (3 (a + 2)))$

Step 3.3.2

Cancel the common factor.

$\frac{1}{a + 1} \cdot ((a + 1) (3 (a + 2)))$

Step 3.3.3

Rewrite the expression.

$3 (a + 2)$

Step 3.4

Apply the distributive property.

$3 a + 3 \cdot 2$

Step 3.5

Multiply $3$ by $2$ .

$3 a + 6$