Factor Factor: 49d^2n-25n

Factor: $49 d^{2} n - 25 n$

Step 1

Factor $n$ out of $49 d^{2} n - 25 n$ .

Factor $n$ out of $49 d^{2} n$ .

$n (49 d^{2}) - 25 n$

Factor $n$ out of $- 25 n$ .

$n (49 d^{2}) + n \cdot - 25$

Factor $n$ out of $n (49 d^{2}) + n \cdot - 25$ .

$n (49 d^{2} - 25)$

Step 2

Rewrite $49 d^{2}$ as ${(7 d)}^{2}$ .

$n ({(7 d)}^{2} - 25)$

Step 3

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

$n ({(7 d)}^{2} - 5^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 d$ and $b = 5$ .

$n ((7 d + 5) (7 d - 5))$

Remove unnecessary parentheses.

$n (7 d + 5) (7 d - 5)$