Algebra Examples

$\frac{8 x y^{2} - 14 y^{2}}{2 y}$

Step 1

Factor $2 y^{2}$ out of $8 x y^{2} - 14 y^{2}$ .

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Step 1.1

Factor $2 y^{2}$ out of $8 x y^{2}$ .

$\frac{2 y^{2} (4 x) - 14 y^{2}}{2 y}$

Step 1.2

Factor $2 y^{2}$ out of $- 14 y^{2}$ .

$\frac{2 y^{2} (4 x) + 2 y^{2} (- 7)}{2 y}$

Step 1.3

Factor $2 y^{2}$ out of $2 y^{2} (4 x) + 2 y^{2} (- 7)$ .

$\frac{2 y^{2} (4 x - 7)}{2 y}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{2 y^{2} (4 x - 7)}{2 y}$

Step 2.2

Rewrite the expression.

$\frac{y^{2} (4 x - 7)}{y}$

Step 3

Cancel the common factor of $y^{2}$ and $y$ .

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Step 3.1

Factor $y$ out of $y^{2} (4 x - 7)$ .

$\frac{y (y (4 x - 7))}{y}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{y (y (4 x - 7))}{y^{1}}$

Step 3.2.2

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

$\frac{y (y (4 x - 7))}{y \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{y (y (4 x - 7))}{y \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{y (4 x - 7)}{1}$

Step 3.2.5

Divide $y (4 x - 7)$ by $1$ .

$y (4 x - 7)$

Step 4

Apply the distributive property.

$y (4 x) + y \cdot - 7$

Step 5

Rewrite using the commutative property of multiplication.

$4 y x + y \cdot - 7$

Step 6

Move $- 7$ to the left of $y$ .

$4 y x - 7 y$