Finite Math Examples

$a x^{3} + 2 b x^{3} - a x y^{2} - 2 b x y^{2}$

Step 1

Factor $x$ out of $a x^{3} + 2 b x^{3} - a x y^{2} - 2 b x y^{2}$ .

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Step 1.1

Factor $x$ out of $a x^{3}$ .

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

Step 1.2

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

$x (a x^{2}) + x (2 b x^{2}) - a x y^{2} - 2 b x y^{2}$

Step 1.3

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

$x (a x^{2}) + x (2 b x^{2}) + x (- a y^{2}) - 2 b x y^{2}$

Step 1.4

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

$x (a x^{2}) + x (2 b x^{2}) + x (- a y^{2}) + x (- 2 b y^{2})$

Step 1.5

Factor $x$ out of $x (a x^{2}) + x (2 b x^{2})$ .

$x (a x^{2} + 2 b x^{2}) + x (- a y^{2}) + x (- 2 b y^{2})$

Step 1.6

Factor $x$ out of $x (a x^{2} + 2 b x^{2}) + x (- a y^{2})$ .

$x (a x^{2} + 2 b x^{2} - a y^{2}) + x (- 2 b y^{2})$

Step 1.7

Factor $x$ out of $x (a x^{2} + 2 b x^{2} - a y^{2}) + x (- 2 b y^{2})$ .

$x (a x^{2} + 2 b x^{2} - a y^{2} - 2 b y^{2})$

Step 2

Factor out the greatest common factor from each group.

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Step 2.1

Group the first two terms and the last two terms.

$x ((a x^{2} + 2 b x^{2}) - a y^{2} - 2 b y^{2})$

Step 2.2

Factor out the greatest common factor (GCF) from each group.

$x (x^{2} (a + 2 b) - y^{2} (a + 2 b))$

Step 3

Factor the polynomial by factoring out the greatest common factor, $a + 2 b$ .

$x ((a + 2 b) (x^{2} - y^{2}))$

Step 4

Factor.

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Step 4.1

Factor.

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Step 4.1.1

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 $b = y$ .

$x ((a + 2 b) ((x + y) (x - y)))$

Step 4.1.2

Remove unnecessary parentheses.

$x ((a + 2 b) (x + y) (x - y))$

Step 4.2

Remove unnecessary parentheses.

$x (a + 2 b) (x + y) (x - y)$