Finite Math Examples

$3 y^{2} - 75 x^{2}$

Step 1

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

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Step 1.1

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

$3 (y^{2}) - 75 x^{2}$

Step 1.2

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

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

Step 1.3

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

$3 (y^{2} - 25 x^{2})$

Step 2

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

$3 (y^{2} - {(5 x)}^{2})$

Step 3

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

$3 ((y + 5 x) (y - (5 x)))$

Step 4

Factor.

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Step 4.1

Multiply $5$ by $- 1$ .

$3 ((y + 5 x) (y - 5 x))$

Step 4.2

Remove unnecessary parentheses.

$3 (y + 5 x) (y - 5 x)$