Finite Math Examples

$18 n^{4} - 60 n^{2} + 50$

Step 1

Factor $2$ out of $18 n^{4} - 60 n^{2} + 50$ .

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Step 1.1

Factor $2$ out of $18 n^{4}$ .

$2 (9 n^{4}) - 60 n^{2} + 50$

Step 1.2

Factor $2$ out of $- 60 n^{2}$ .

$2 (9 n^{4}) + 2 (- 30 n^{2}) + 50$

Step 1.3

Factor $2$ out of $50$ .

$2 (9 n^{4}) + 2 (- 30 n^{2}) + 2 (25)$

Step 1.4

Factor $2$ out of $2 (9 n^{4}) + 2 (- 30 n^{2})$ .

$2 (9 n^{4} - 30 n^{2}) + 2 (25)$

Step 1.5

Factor $2$ out of $2 (9 n^{4} - 30 n^{2}) + 2 (25)$ .

$2 (9 n^{4} - 30 n^{2} + 25)$

Step 2

Rewrite $n^{4}$ as ${(n^{2})}^{2}$ .

$2 (9 {(n^{2})}^{2} - 30 n^{2} + 25)$

Step 3

Let $u = n^{2}$ . Substitute $u$ for all occurrences of $n^{2}$ .

$2 (9 u^{2} - 30 u + 25)$

Step 4

Factor using the perfect square rule.

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Step 4.1

Rewrite $9 u^{2}$ as ${(3 u)}^{2}$ .

$2 ({(3 u)}^{2} - 30 u + 25)$

Step 4.2

Rewrite $25$ as $5^{2}$ .

$2 ({(3 u)}^{2} - 30 u + 5^{2})$

Step 4.3

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

$30 u = 2 \cdot (3 u) \cdot 5$

Step 4.4

Rewrite the polynomial.

$2 ({(3 u)}^{2} - 2 \cdot (3 u) \cdot 5 + 5^{2})$

Step 4.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 u$ and $b = 5$ .

$2 {(3 u - 5)}^{2}$

Step 5

Replace all occurrences of $u$ with $n^{2}$ .

$2 {(3 n^{2} - 5)}^{2}$