Basic Math Examples

$(y^{2} - 49) \cdot \frac{9}{y - 7}$

Step 1

Multiply $y^{2} - 49$ by $\frac{9}{y - 7}$ .

$\frac{(y^{2} - 49) \cdot 9}{y - 7}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{(y^{2} - 7^{2}) \cdot 9}{y - 7}$

Step 2.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = y$ and $b = 7$ .

$\frac{(y + 7) (y - 7) \cdot 9}{y - 7}$

Step 3

Simplify terms.

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Step 3.1

Cancel the common factor of $y - 7$ .

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Step 3.1.1

Cancel the common factor.

$\frac{(y + 7) (y - 7) \cdot 9}{y - 7}$

Step 3.1.2

Divide $(y + 7) \cdot 9$ by $1$ .

$(y + 7) \cdot 9$

Step 3.2

Apply the distributive property.

$y \cdot 9 + 7 \cdot 9$

Step 3.3

Simplify the expression.

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Step 3.3.1

Move $9$ to the left of $y$ .

$9 \cdot y + 7 \cdot 9$

Step 3.3.2

Multiply $7$ by $9$ .

$9 y + 63$