Pre-Algebra Examples

$147 x^{2} y - 27 y$

Step 1

Factor $3 y$ out of $147 x^{2} y - 27 y$ .

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Step 1.1

Factor $3 y$ out of $147 x^{2} y$ .

$3 y (49 x^{2}) - 27 y$

Step 1.2

Factor $3 y$ out of $- 27 y$ .

$3 y (49 x^{2}) + 3 y (- 9)$

Step 1.3

Factor $3 y$ out of $3 y (49 x^{2}) + 3 y (- 9)$ .

$3 y (49 x^{2} - 9)$

Step 2

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

$3 y ({(7 x)}^{2} - 9)$

Step 3

Rewrite $9$ as $3^{2}$ .

$3 y ({(7 x)}^{2} - 3^{2})$

Step 4

Factor.

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Step 4.1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 x$ and $b = 3$ .

$3 y ((7 x + 3) (7 x - 3))$

Step 4.2

Remove unnecessary parentheses.

$3 y (7 x + 3) (7 x - 3)$