Basic Math Examples

$4 c^{2} + 20 c + 16$

Step 1

Factor

$4$ out of

$4 c^{2} + 20 c + 16$ .

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Step 1.1

Factor

$4$ out of

$4 c^{2}$ .

$4 (c^{2}) + 20 c + 16$

Step 1.2

Factor

$4$ out of

$20 c$ .

$4 (c^{2}) + 4 (5 c) + 16$

Step 1.3

Factor

$4$ out of

$16$ .

$4 c^{2} + 4 (5 c) + 4 \cdot 4$

Step 1.4

Factor

$4$ out of

$4 c^{2} + 4 (5 c)$ .

$4 (c^{2} + 5 c) + 4 \cdot 4$

Step 1.5

Factor

$4$ out of

$4 (c^{2} + 5 c) + 4 \cdot 4$ .

$4 (c^{2} + 5 c + 4)$

$4 (c^{2} + 5 c + 4)$

Step 2

Factor.

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Step 2.1

Factor

$c^{2} + 5 c + 4$ using the AC method.

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Step 2.1.1

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

$4$ and whose sum is

$5$ .

$1, 4$

Step 2.1.2

Write the factored form using these integers.

$4 ((c + 1) (c + 4))$

$4 ((c + 1) (c + 4))$

Step 2.2

Remove unnecessary parentheses.

$4 (c + 1) (c + 4)$

$4 (c + 1) (c + 4)$

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