Factor 3x^4-75x^2=0

$3 x^{4} - 75 x^{2} = 0$

Step 1

Factor $3 x^{2}$ out of $3 x^{4} - 75 x^{2}$ .

Factor $3 x^{2}$ out of $3 x^{4}$ .

$3 x^{2} (x^{2}) - 75 x^{2} = 0$

Factor $3 x^{2}$ out of $- 75 x^{2}$ .

$3 x^{2} (x^{2}) + 3 x^{2} (- 25) = 0$

Factor $3 x^{2}$ out of $3 x^{2} (x^{2}) + 3 x^{2} (- 25)$ .

$3 x^{2} (x^{2} - 25) = 0$

Step 2

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

$3 x^{2} (x^{2} - 5^{2}) = 0$

Step 3

Factor.

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

$3 x^{2} ((x + 5) (x - 5)) = 0$

Remove unnecessary parentheses.

$3 x^{2} (x + 5) (x - 5) = 0$