Basic Math Examples

$147 r^{2} - 75 s^{2}$

Step 1

Factor $3$ out of $147 r^{2} - 75 s^{2}$ .

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Step 1.1

Factor $3$ out of $147 r^{2}$ .

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

Step 1.2

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

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

Step 1.3

Factor $3$ out of $3 (49 r^{2}) + 3 (- 25 s^{2})$ .

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

Step 2

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

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

Step 3

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

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

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 $b = 5 s$ .

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

Step 5

Factor.

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Step 5.1

Multiply $5$ by $- 1$ .

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

Step 5.2

Remove unnecessary parentheses.

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