Basic Math Examples

$16 y^{4} + 12 y^{3} + 2 y^{2}$

Step 1

Factor $2 y^{2}$ out of $16 y^{4} + 12 y^{3} + 2 y^{2}$ .

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Step 1.1

Factor $2 y^{2}$ out of $16 y^{4}$ .

$2 y^{2} (8 y^{2}) + 12 y^{3} + 2 y^{2}$

Step 1.2

Factor $2 y^{2}$ out of $12 y^{3}$ .

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

Step 1.3

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

$2 y^{2} (8 y^{2}) + 2 y^{2} (6 y) + 2 y^{2} (1)$

Step 1.4

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

$2 y^{2} (8 y^{2} + 6 y) + 2 y^{2} (1)$

Step 1.5

Factor $2 y^{2}$ out of $2 y^{2} (8 y^{2} + 6 y) + 2 y^{2} (1)$ .

$2 y^{2} (8 y^{2} + 6 y + 1)$

Step 2

Factor.

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Step 2.1

Factor by grouping.

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Step 2.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 8 \cdot 1 = 8$ and whose sum is $b = 6$ .

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Step 2.1.1.1

Factor $6$ out of $6 y$ .

$2 y^{2} (8 y^{2} + 6 (y) + 1)$

Step 2.1.1.2

Rewrite $6$ as $2$ plus $4$

$2 y^{2} (8 y^{2} + (2 + 4) y + 1)$

Step 2.1.1.3

Apply the distributive property.

$2 y^{2} (8 y^{2} + 2 y + 4 y + 1)$

Step 2.1.2

Factor out the greatest common factor from each group.

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Step 2.1.2.1

Group the first two terms and the last two terms.

$2 y^{2} ((8 y^{2} + 2 y) + 4 y + 1)$

Step 2.1.2.2

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

$2 y^{2} (2 y (4 y + 1) + 1 (4 y + 1))$

Step 2.1.3

Factor the polynomial by factoring out the greatest common factor, $4 y + 1$ .

$2 y^{2} ((4 y + 1) (2 y + 1))$

Step 2.2

Remove unnecessary parentheses.

$2 y^{2} (4 y + 1) (2 y + 1)$