Let's simplify the expression step by step to determine which option (a, b, or c) is correct.
The expression we are starting with is:
\(-3(-3x + 4y - 10) + 6y\)
First, distribute the -3:
\[ -3 \cdot -3x + -3 \cdot 4y + -3 \cdot -10 = 9x - 12y + 30 \]
Now we add \(6y\):
\[ 9x - 12y + 30 + 6y \]
Combine like terms (\(-12y + 6y\)):
\[ 9x + (-12y + 6y) + 30 = 9x - 6y + 30 \]
So the final simplified expression is:
\[ 9x - 6y + 30 \]
Now let's compare that with the given options:
- a) \(9x + 6y + 30\)
- b) \(9x - 6y + 30\)
- c) \(9x - 6y - 30\)
The correct answer is b) \(9x - 6y + 30\).