Pre-Algebra Examples

$x^{3} y^{2} + x^{2} y - 12 x$

Step 1

Factor $x$ out of $x^{3} y^{2} + x^{2} y - 12 x$ .

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Step 1.1

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

$x (x^{2} y^{2}) + x^{2} y - 12 x$

Step 1.2

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

$x (x^{2} y^{2}) + x (x y) - 12 x$

Step 1.3

Factor $x$ out of $- 12 x$ .

$x (x^{2} y^{2}) + x (x y) + x \cdot - 12$

Step 1.4

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

$x (x^{2} y^{2} + x y) + x \cdot - 12$

Step 1.5

Factor $x$ out of $x (x^{2} y^{2} + x y) + x \cdot - 12$ .

$x (x^{2} y^{2} + x y - 12)$

Step 2

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

$x ({(x y)}^{2} + x y - 12)$

Step 3

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$x (u^{2} + u - 12)$

Step 4

Factor $u^{2} + u - 12$ using the AC method.

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Step 4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 12$ and whose sum is $1$ .

$- 3, 4$

Step 4.2

Write the factored form using these integers.

$x ((u - 3) (u + 4))$

Step 5

Factor.

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Step 5.1

Replace all occurrences of $u$ with $x y$ .

$x ((x y - 3) (x y + 4))$

Step 5.2

Remove unnecessary parentheses.

$x (x y - 3) (x y + 4)$