Pre-Algebra Examples

$48 n^{3} - 24 n^{2} + 3 n$

Step 1

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

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Step 1.1

Factor $3 n$ out of $48 n^{3}$ .

$3 n (16 n^{2}) - 24 n^{2} + 3 n$

Step 1.2

Factor $3 n$ out of $- 24 n^{2}$ .

$3 n (16 n^{2}) + 3 n (- 8 n) + 3 n$

Step 1.3

Factor $3 n$ out of $3 n$ .

$3 n (16 n^{2}) + 3 n (- 8 n) + 3 n (1)$

Step 1.4

Factor $3 n$ out of $3 n (16 n^{2}) + 3 n (- 8 n)$ .

$3 n (16 n^{2} - 8 n) + 3 n (1)$

Step 1.5

Factor $3 n$ out of $3 n (16 n^{2} - 8 n) + 3 n (1)$ .

$3 n (16 n^{2} - 8 n + 1)$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $16 n^{2}$ as ${(4 n)}^{2}$ .

$3 n ({(4 n)}^{2} - 8 n + 1)$

Step 2.2

Rewrite $1$ as $1^{2}$ .

$3 n ({(4 n)}^{2} - 8 n + 1^{2})$

Step 2.3

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

$8 n = 2 \cdot (4 n) \cdot 1$

Step 2.4

Rewrite the polynomial.

$3 n ({(4 n)}^{2} - 2 \cdot (4 n) \cdot 1 + 1^{2})$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 4 n$ and $b = 1$ .

$3 n {(4 n - 1)}^{2}$