Finite Math Examples

$3 p^{2} q^{2} + 9 p^{2} q + 12 p q^{2} + 36 p q$

Step 1

Factor $3 p q$ out of $3 p^{2} q^{2} + 9 p^{2} q + 12 p q^{2} + 36 p q$ .

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Step 1.1

Factor $3 p q$ out of $3 p^{2} q^{2}$ .

$3 p q (p q) + 9 p^{2} q + 12 p q^{2} + 36 p q$

Step 1.2

Factor $3 p q$ out of $9 p^{2} q$ .

$3 p q (p q) + 3 p q (3 p) + 12 p q^{2} + 36 p q$

Step 1.3

Factor $3 p q$ out of $12 p q^{2}$ .

$3 p q (p q) + 3 p q (3 p) + 3 p q (4 q) + 36 p q$

Step 1.4

Factor $3 p q$ out of $36 p q$ .

$3 p q (p q) + 3 p q (3 p) + 3 p q (4 q) + 3 p q (12)$

Step 1.5

Factor $3 p q$ out of $3 p q (p q) + 3 p q (3 p)$ .

$3 p q (p q + 3 p) + 3 p q (4 q) + 3 p q (12)$

Step 1.6

Factor $3 p q$ out of $3 p q (p q + 3 p) + 3 p q (4 q)$ .

$3 p q (p q + 3 p + 4 q) + 3 p q (12)$

Step 1.7

Factor $3 p q$ out of $3 p q (p q + 3 p + 4 q) + 3 p q (12)$ .

$3 p q (p q + 3 p + 4 q + 12)$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$3 p q ((p q + 3 p) + 4 q + 12)$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$3 p q (p (q + 3) + 4 (q + 3))$

Step 3

Factor.

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Step 3.1

Factor the polynomial by factoring out the greatest common factor, $q + 3$ .

$3 p q ((q + 3) (p + 4))$

Step 3.2

Remove unnecessary parentheses.

$3 p q (q + 3) (p + 4)$