Algebra Examples

$\frac{5 k + 4}{2 k + 6} \cdot (k^{2} + 7 k + 12)$

Step 1

Factor $2$ out of $2 k + 6$ .

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Step 1.1

Factor $2$ out of $2 k$ .

$\frac{5 k + 4}{2 (k) + 6} \cdot (k^{2} + 7 k + 12)$

Step 1.2

Factor $2$ out of $6$ .

$\frac{5 k + 4}{2 k + 2 \cdot 3} \cdot (k^{2} + 7 k + 12)$

Step 1.3

Factor $2$ out of $2 k + 2 \cdot 3$ .

$\frac{5 k + 4}{2 (k + 3)} \cdot (k^{2} + 7 k + 12)$

Step 2

Multiply $\frac{5 k + 4}{2 (k + 3)}$ by $k^{2} + 7 k + 12$ .

$\frac{(5 k + 4) (k^{2} + 7 k + 12)}{2 (k + 3)}$

Step 3

Factor $k^{2} + 7 k + 12$ 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 $12$ and whose sum is $7$ .

$3, 4$

Step 3.2

Write the factored form using these integers.

$\frac{(5 k + 4) ((k + 3) (k + 4))}{2 (k + 3)}$

$\frac{(5 k + 4) (k + 3) (k + 4)}{2 (k + 3)}$

Step 4

Cancel the common factor of $k + 3$ .

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Step 4.1

Cancel the common factor.

$\frac{(5 k + 4) (k + 3) (k + 4)}{2 (k + 3)}$

Step 4.2

Rewrite the expression.

$\frac{(5 k + 4) (k + 4)}{2}$