To simplify the given expression, let's break it down step-by-step:
1. Distribute the negative sign to every term inside the parentheses:
-(a - 2b - 2(2a - 3b - c))
This becomes:
-a + 26 + 4a - 6b + 2c
2. Combine like terms:
(-a + 4a) + (2b - 6b) + 2c
This simplifies to:
3a - 4b + 2c
So, the simplified expression is 3a - 4b + 2c.
Here's an example to help illustrate the steps:
Let's say a = 2, b = 3, and c = 1. Plugging these values into the original expression:
2a b 3c - (a-2b-2(2a-3b-c))
We get:
2(2)(3)3 - (2 - 2(2)(2 - 3(3) - 1))
Simplifying further:
72 - (2 - 2(2)(2 - 9 - 1))
Now:
72 - (2 - 2(2)(-8))
Expanding the second term:
72 - (2 - 2(-16)
72 - (2 + 32)
72 - 34
Resulting in:
38
So, when a = 2, b = 3, and c = 1, the simplified expression evaluates to 38.