Sure! Let's break down the expression step-by-step.
We start with the expression:
[tex]\[ (-4 b m + 1) - (-5 - 10 b m + 1) \][/tex]
We need to distribute the subtraction through the second set of parentheses. When we do this, we also need to account for the signs in front of each term inside the parentheses. Let's distribute the negative sign:
1. The original expression is:
[tex]\[ (-4 b m + 1) - (-5 - 10 b m + 1) \][/tex]
2. Distribute the negative sign through the second parenthesis:
[tex]\[ = (-4 b m + 1) - (-5) - (-10 b m) - 1 \][/tex]
Which simplifies to:
[tex]\[ = (-4 b m + 1) + 5 + 10 b m - 1 \][/tex]
3. Now, combine like terms:
- Combine the [tex]\( b m \)[/tex] terms:
[tex]\[ (-4 b m + 10 b m) = 6 b m \][/tex]
- Combine the constant terms:
[tex]\[ (1 - 1 + 5) = 5 \][/tex]
4. Put it all together:
[tex]\[ 6 b m + 5 \][/tex]
So the simplified expression is:
[tex]\[ \boxed{6 b m + 5} \][/tex]
