Fractorise:
`(3x-4y)^(2) - 25z ^(2)`

Answer

To factorize the expression \((3x - 4y)^2 - 25z^2\), we can follow these steps:

### Step 1: Identify the structure of the expression
The expression \((3x - 4y)^2 - 25z^2\) is in the form of \(a^2 - b^2\), where:
- \(a = 3x - 4y\)
- \(b = 5z\) (since \(25z^2 = (5z)^2\))

### Step 2: Apply the difference of squares formula
The difference of squares can be factored using the formula:
\[ a^2 - b^2 = (a + b)(a - b) \]
Substituting our values for \(a\) and \(b\):
\[ (3x - 4y)^2 - (5z)^2 = (3x - 4y + 5z)(3x - 4y - 5z) \]

### Step 3: Write the final factored form
Thus, the factored form of the expression is:
\[ (3x - 4y + 5z)(3x - 4y - 5z) \]

### Final Answer:
\[ (3x - 4y + 5z)(3x - 4y - 5z) \]

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