Finite Math Examples

$147 r^{2} - 75$

Step 1

Factor out the GCF of $3$ from $147 r^{2} - 75$ .

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Step 1.1

Factor out the GCF of $3$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $3$ from the expression $147 r^{2}$ .

$3 (49 r^{2}) - 75$

Step 1.1.2

Factor out the GCF of $3$ from the expression $- 75$ .

$3 (49 r^{2}) + 3 (- 25)$

Step 1.2

Since all the terms share a common factor of $3$ , it can be factored out of each term.

$3 (49 r^{2} - 25)$

Step 2

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

$3 ({(7 r)}^{2} - 25)$

Step 3

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

$3 ({(7 r)}^{2} - 5^{2})$

Step 4

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

$3 ((7 r + 5) (7 r - 5))$