Basic Math Examples

$\frac{k^{2} + 10 k + 16}{k^{2} + 13 + 40} \cdot \frac{k^{2} + 5 k}{k^{2} - 2 k - 8}$

Step 1

Factor $k^{2} + 10 k + 16$ using the AC method.

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Step 1.1

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 $16$ and whose sum is $10$ .

$2, 8$

Step 1.2

Write the factored form using these integers.

$\frac{(k + 2) (k + 8)}{k^{2} + 13 + 40} \cdot \frac{k^{2} + 5 k}{k^{2} - 2 k - 8}$

Step 2

Add $13$ and $40$ .

$\frac{(k + 2) (k + 8)}{k^{2} + 53} \cdot \frac{k^{2} + 5 k}{k^{2} - 2 k - 8}$

Step 3

Factor $k$ out of $k^{2} + 5 k$ .

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Step 3.1

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

$\frac{(k + 2) (k + 8)}{k^{2} + 53} \cdot \frac{k \cdot k + 5 k}{k^{2} - 2 k - 8}$

Step 3.2

Factor $k$ out of $5 k$ .

$\frac{(k + 2) (k + 8)}{k^{2} + 53} \cdot \frac{k \cdot k + k \cdot 5}{k^{2} - 2 k - 8}$

Step 3.3

Factor $k$ out of $k \cdot k + k \cdot 5$ .

$\frac{(k + 2) (k + 8)}{k^{2} + 53} \cdot \frac{k (k + 5)}{k^{2} - 2 k - 8}$

Step 4

Factor $k^{2} - 2 k - 8$ using the AC method.

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Step 4.1

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 $- 8$ and whose sum is $- 2$ .

$- 4, 2$

Step 4.2

Write the factored form using these integers.

$\frac{(k + 2) (k + 8)}{k^{2} + 53} \cdot \frac{k (k + 5)}{(k - 4) (k + 2)}$