Finite Math Examples

$\frac{x^{2}}{9} + \frac{{(y - 8)}^{2}}{169}$

Step 1

To write $\frac{x^{2}}{9}$ as a fraction with a common denominator, multiply by $\frac{169}{169}$ .

$\frac{x^{2}}{9} \cdot \frac{169}{169} + \frac{{(y - 8)}^{2}}{169}$

Step 2

To write $\frac{{(y - 8)}^{2}}{169}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{x^{2}}{9} \cdot \frac{169}{169} + \frac{{(y - 8)}^{2}}{169} \cdot \frac{9}{9}$

Step 3

Write each expression with a common denominator of $1521$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x^{2}}{9}$ by $\frac{169}{169}$ .

$\frac{x^{2} \cdot 169}{9 \cdot 169} + \frac{{(y - 8)}^{2}}{169} \cdot \frac{9}{9}$

Step 3.2

Multiply $9$ by $169$ .

$\frac{x^{2} \cdot 169}{1521} + \frac{{(y - 8)}^{2}}{169} \cdot \frac{9}{9}$

Step 3.3

Multiply $\frac{{(y - 8)}^{2}}{169}$ by $\frac{9}{9}$ .

$\frac{x^{2} \cdot 169}{1521} + \frac{{(y - 8)}^{2} \cdot 9}{169 \cdot 9}$

Step 3.4

Multiply $169$ by $9$ .

$\frac{x^{2} \cdot 169}{1521} + \frac{{(y - 8)}^{2} \cdot 9}{1521}$

Step 4

Combine the numerators over the common denominator.

$\frac{x^{2} \cdot 169 + {(y - 8)}^{2} \cdot 9}{1521}$

Step 5

Simplify the numerator.

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Step 5.1

Move $169$ to the left of $x^{2}$ .

$\frac{169 \cdot x^{2} + {(y - 8)}^{2} \cdot 9}{1521}$

Step 5.2

Rewrite ${(y - 8)}^{2}$ as $(y - 8) (y - 8)$ .

$\frac{169 x^{2} + (y - 8) (y - 8) \cdot 9}{1521}$

Step 5.3

Expand $(y - 8) (y - 8)$ using the FOIL Method.

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Step 5.3.1

Apply the distributive property.

$\frac{169 x^{2} + (y (y - 8) - 8 (y - 8)) \cdot 9}{1521}$

Step 5.3.2

Apply the distributive property.

$\frac{169 x^{2} + (y \cdot y + y \cdot - 8 - 8 (y - 8)) \cdot 9}{1521}$

Step 5.3.3

Apply the distributive property.

$\frac{169 x^{2} + (y \cdot y + y \cdot - 8 - 8 y - 8 \cdot - 8) \cdot 9}{1521}$

Step 5.4

Simplify and combine like terms.

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Step 5.4.1

Simplify each term.

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Step 5.4.1.1

Multiply $y$ by $y$ .

$\frac{169 x^{2} + (y^{2} + y \cdot - 8 - 8 y - 8 \cdot - 8) \cdot 9}{1521}$

Step 5.4.1.2

Move $- 8$ to the left of $y$ .

$\frac{169 x^{2} + (y^{2} - 8 \cdot y - 8 y - 8 \cdot - 8) \cdot 9}{1521}$

Step 5.4.1.3

Multiply $- 8$ by $- 8$ .

$\frac{169 x^{2} + (y^{2} - 8 y - 8 y + 64) \cdot 9}{1521}$

Step 5.4.2

Subtract $8 y$ from $- 8 y$ .

$\frac{169 x^{2} + (y^{2} - 16 y + 64) \cdot 9}{1521}$

Step 5.5

Apply the distributive property.

$\frac{169 x^{2} + y^{2} \cdot 9 - 16 y \cdot 9 + 64 \cdot 9}{1521}$

Step 5.6

Simplify.

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Step 5.6.1

Move $9$ to the left of $y^{2}$ .

$\frac{169 x^{2} + 9 \cdot y^{2} - 16 y \cdot 9 + 64 \cdot 9}{1521}$

Step 5.6.2

Multiply $9$ by $- 16$ .

$\frac{169 x^{2} + 9 \cdot y^{2} - 144 y + 64 \cdot 9}{1521}$

Step 5.6.3

Multiply $64$ by $9$ .

$\frac{169 x^{2} + 9 \cdot y^{2} - 144 y + 576}{1521}$

$\frac{169 x^{2} + 9 y^{2} - 144 y + 576}{1521}$