Simplify the expression: (2m-3n)² - m(5m-n)

Expression Simplification:

• Expression: (2m - 3n)² - m(5m - n)

Step-by-step solution:

1. Step 1: Expand the squared term (2m - 3n)².
   Using the formula (a - b)² = a² - 2ab + b²:
   \[ (2m - 3n)² = (2m)² - 2(2m)(3n) + (3n)² \]
   \[ = 4m² - 12mn + 9n² \]
2. Step 2: Distribute m into the second term -m(5m - n).
   \[ -m(5m - n) = -5m² + mn \]
3. Step 3: Combine the expanded terms.
   Now, substitute the expanded parts back into the original expression:
   \[ (4m² - 12mn + 9n²) + (-5m² + mn) \]
4. Step 4: Combine like terms.
   Combine the m² terms: 4m² - 5m² = -m²
   Combine the mn terms: -12mn + mn = -11mn
   The n² term remains: 9n²
   \[ -m² - 11mn + 9n² \]

Answer: -m² - 11mn + 9n²