Sure, let's simplify the given expression step-by-step.
Given expression:
[tex]\[ E = -4(10b - 10c) + 9c - 10(-4c + 3b) \][/tex]
### Step 1: Distribute the constants inside the parentheses
First, distribute [tex]\(-4\)[/tex] inside [tex]\( (10b - 10c) \)[/tex]:
[tex]\[ -4 \cdot 10b - (-4 \cdot 10c) = -40b + 40c \][/tex]
Next, distribute [tex]\(-10\)[/tex] inside [tex]\( (-4c + 3b) \)[/tex]:
[tex]\[ -10 \cdot (-4c) + (-10 \cdot 3b) = 40c - 30b \][/tex]
Substituting these simplified forms back into the expression, we get:
[tex]\[ E = -40b + 40c + 9c + 40c - 30b \][/tex]
### Step 2: Combine like terms
Combine the terms with [tex]\( b \)[/tex] and the terms with [tex]\( c \)[/tex]:
1. Terms with [tex]\( b \)[/tex]:
[tex]\[ -40b - 30b = -70b \][/tex]
2. Terms with [tex]\( c \)[/tex]:
[tex]\[ 40c + 40c + 9c = 89c \][/tex]
### Step 3: Write the simplified expression
Combining the simplified [tex]\( b \)[/tex] terms and [tex]\( c \)[/tex] terms, we get:
[tex]\[ E = -70b + 89c \][/tex]
Thus, the simplified expression is:
[tex]\[ -70b + 89c \][/tex]
