Finite Math Examples

$- 23 x y^{2} + 11 x y^{2} - 12 x y \cdot y^{2}$

Step 1

Add $- 23 x y^{2}$ and $11 x y^{2}$ .

$- 12 x y^{2} - 12 x y \cdot y^{2}$

Step 2

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

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Step 2.1

Reorder $- 12 x y^{2}$ and $- 12 x y \cdot y^{2}$ .

$- 12 x y \cdot y^{2} - 12 x y^{2}$

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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

Step 3

Factor.

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Step 3.1

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

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Step 3.1.1

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

$- 12 x y (y \cdot y + y)$

Step 3.1.2

Raise $y$ to the power of $1$ .

$- 12 x y (y \cdot y + y^{1})$

Step 3.1.3

Factor $y$ out of $y^{1}$ .

$- 12 x y (y \cdot y + y \cdot 1)$

Step 3.1.4

Factor $y$ out of $y \cdot y + y \cdot 1$ .

$- 12 x y (y (y + 1))$

Step 3.2

Remove unnecessary parentheses.

$- 12 x y \cdot y (y + 1)$

Step 4

Combine exponents.

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Step 4.1

Raise $y$ to the power of $1$ .

$- 12 x (y^{1} y) (y + 1)$

Step 4.2

Raise $y$ to the power of $1$ .

$- 12 x (y^{1} y^{1}) (y + 1)$

Step 4.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 12 x y^{1 + 1} (y + 1)$

Step 4.4

Add $1$ and $1$ .

$- 12 x y^{2} (y + 1)$