Finite Math Examples

$3 y^{2} + 24 y + 48$

Step 1

Factor $3$ out of $3 y^{2} + 24 y + 48$ .

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Step 1.1

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

$3 (y^{2}) + 24 y + 48$

Step 1.2

Factor $3$ out of $24 y$ .

$3 (y^{2}) + 3 (8 y) + 48$

Step 1.3

Factor $3$ out of $48$ .

$3 y^{2} + 3 (8 y) + 3 \cdot 16$

Step 1.4

Factor $3$ out of $3 y^{2} + 3 (8 y)$ .

$3 (y^{2} + 8 y) + 3 \cdot 16$

Step 1.5

Factor $3$ out of $3 (y^{2} + 8 y) + 3 \cdot 16$ .

$3 (y^{2} + 8 y + 16)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16$ as $4^{2}$ .

$3 (y^{2} + 8 y + 4^{2})$

Step 2.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 y = 2 \cdot y \cdot 4$

Step 2.3

Rewrite the polynomial.

$3 (y^{2} + 2 \cdot y \cdot 4 + 4^{2})$

Step 2.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 4$ .

$3 {(y + 4)}^{2}$