Basic Math Examples

$y^{2} + 12 y + 16 + y^{2}$

Step 1

Add $y^{2}$ and $y^{2}$ .

$2 y^{2} + 12 y + 16$

Step 2

Factor $2$ out of $2 y^{2} + 12 y + 16$ .

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Step 2.1

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

$2 (y^{2}) + 12 y + 16$

Step 2.2

Factor $2$ out of $12 y$ .

$2 (y^{2}) + 2 (6 y) + 16$

Step 2.3

Factor $2$ out of $16$ .

$2 y^{2} + 2 (6 y) + 2 \cdot 8$

Step 2.4

Factor $2$ out of $2 y^{2} + 2 (6 y)$ .

$2 (y^{2} + 6 y) + 2 \cdot 8$

Step 2.5

Factor $2$ out of $2 (y^{2} + 6 y) + 2 \cdot 8$ .

$2 (y^{2} + 6 y + 8)$

Step 3

Factor.

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Step 3.1

Factor $y^{2} + 6 y + 8$ using the AC method.

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Step 3.1.1

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 $8$ and whose sum is $6$ .

$2, 4$

Step 3.1.2

Write the factored form using these integers.

$2 ((y + 2) (y + 4))$

Step 3.2

Remove unnecessary parentheses.

$2 (y + 2) (y + 4)$