Fractorise the
`(y ^(2))/( 9) - 9`

Answer

To factorize the expression \(\frac{y^2}{9} - 9\), we can follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{y^2}{9} - 9 \]
We can express \(9\) as \(\frac{81}{9}\) to have a common denominator:
\[ \frac{y^2}{9} - \frac{81}{9} \]

### Step 2: Combine the fractions
Now that we have a common denominator, we can combine the two fractions:
\[ \frac{y^2 - 81}{9} \]

### Step 3: Recognize the difference of squares
The numerator \(y^2 - 81\) can be recognized as a difference of squares, which follows the identity:
\[ a^2 - b^2 = (a - b)(a + b) \]
Here, \(a = y\) and \(b = 9\). Thus, we can factor it as:
\[ y^2 - 81 = (y - 9)(y + 9) \]

### Step 4: Substitute back into the fraction
Now we substitute this back into our expression:
\[ \frac{(y - 9)(y + 9)}{9} \]

### Step 5: Final factorization
The final factorized form of the expression is:
\[ \frac{(y - 9)(y + 9)}{9} \]

### Summary
The factorized form of \(\frac{y^2}{9} - 9\) is:
\[ \frac{(y - 9)(y + 9)}{9} \]

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