Expand: `(3x- 5y - 2z) (3x- 5y + 2z)`

Answer

To expand the expression \((3x - 5y - 2z)(3x - 5y + 2z)\), we can use the difference of squares formula, which states that \( (a - b)(a + b) = a^2 - b^2 \).

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Let \( a = 3x - 5y \)
- Let \( b = 2z \)

2. **Apply the difference of squares formula**:
\[ (3x - 5y - 2z)(3x - 5y + 2z) = (a - b)(a + b) = a^2 - b^2 \]

3. **Calculate \(a^2\)**:
\[ a^2 = (3x - 5y)^2 = (3x)^2 - 2(3x)(5y) + (5y)^2 \]
\[ = 9x^2 - 30xy + 25y^2 \]

4. **Calculate \(b^2\)**:
\[ b^2 = (2z)^2 = 4z^2 \]

5. **Combine the results**:
\[ a^2 - b^2 = (9x^2 - 30xy + 25y^2) - 4z^2 \]
\[ = 9x^2 - 30xy + 25y^2 - 4z^2 \]

### Final Expanded Form:
\[ (3x - 5y - 2z)(3x - 5y + 2z) = 9x^2 - 30xy + 25y^2 - 4z^2 \]