Algebra Examples

$\frac{2 k + 1}{3 k + 3} \cdot (k^{2} + 6 k + 5)$

Step 1

Factor $3$ out of $3 k + 3$ .

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Step 1.1

Factor $3$ out of $3 k$ .

$\frac{2 k + 1}{3 (k) + 3} \cdot (k^{2} + 6 k + 5)$

Step 1.2

Factor $3$ out of $3$ .

$\frac{2 k + 1}{3 (k) + 3 (1)} \cdot (k^{2} + 6 k + 5)$

Step 1.3

Factor $3$ out of $3 (k) + 3 (1)$ .

$\frac{2 k + 1}{3 (k + 1)} \cdot (k^{2} + 6 k + 5)$

Step 2

Multiply $\frac{2 k + 1}{3 (k + 1)}$ by $k^{2} + 6 k + 5$ .

$\frac{(2 k + 1) (k^{2} + 6 k + 5)}{3 (k + 1)}$

Step 3

Factor $k^{2} + 6 k + 5$ using the AC method.

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Step 3.1

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 $5$ and whose sum is $6$ .

$1, 5$

Step 3.2

Write the factored form using these integers.

$\frac{(2 k + 1) ((k + 1) (k + 5))}{3 (k + 1)}$

$\frac{(2 k + 1) (k + 1) (k + 5)}{3 (k + 1)}$

Step 4

Cancel the common factor of $k + 1$ .

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Step 4.1

Cancel the common factor.

$\frac{(2 k + 1) (k + 1) (k + 5)}{3 (k + 1)}$

Step 4.2

Rewrite the expression.

$\frac{(2 k + 1) (k + 5)}{3}$