To simplify the expression \((9m - 3) - (2m + 12)(9m - 3)\), we'll start by distributing \((2m + 12)\) into \((9m - 3)\) and then simplify the entire expression.
-
First, let's distribute: \[ (2m + 12)(9m - 3) = 2m(9m) + 2m(-3) + 12(9m) + 12(-3) \] \[ = 18m^2 - 6m + 108m - 36 \] \[ = 18m^2 + 102m - 36 \]
-
Now substitute this back into the original expression: \[ (9m - 3) - (18m^2 + 102m - 36) \]
-
This becomes: \[ 9m - 3 - 18m^2 - 102m + 36 \]
-
Now, combine like terms:
- For \(m^2\) terms: \(-18m^2\)
- For \(m\) terms: \(9m - 102m = -93m\)
- For constant terms: \(-3 + 36 = 33\)
So, the simplified expression is: \[ -18m^2 - 93m + 33 \]
Based on the responses given:
- The correct answer must include \(-18m^2\), \(-93m\), and \(+33\).
It seems none of the provided responses exactly matches this simplified expression fully. Please double-check the answer choices provided.
1 answer