Certainly! Let's expand and simplify the given expression step-by-step.
We start with the expression:
[tex]\[ 4(2 - p - q) + 3(4 + p - 2q) \][/tex]
### Step 1: Expand Each Term
1. Expand [tex]\( 4(2 - p - q) \)[/tex]:
[tex]\[ 4(2) - 4(p) - 4(q) = 8 - 4p - 4q \][/tex]
2. Expand [tex]\( 3(4 + p - 2q) \)[/tex]:
[tex]\[ 3(4) + 3(p) - 3(2q) = 12 + 3p - 6q \][/tex]
### Step 2: Combine the Expanded Terms
Now, add the two expanded expressions together:
[tex]\[ (8 - 4p - 4q) + (12 + 3p - 6q) \][/tex]
### Step 3: Combine Like Terms
Combine the constant terms, the terms involving [tex]\( p \)[/tex], and the terms involving [tex]\( q \)[/tex]:
1. Combine the constants:
[tex]\[ 8 + 12 = 20 \][/tex]
2. Combine the [tex]\( p \)[/tex] terms:
[tex]\[ -4p + 3p = -p \][/tex]
3. Combine the [tex]\( q \)[/tex] terms:
[tex]\[ -4q - 6q = -10q \][/tex]
### Step 4: Write the Simplified Expression
Putting it all together, we get the simplified expression:
[tex]\[ 20 - p - 10q \][/tex]
So, the result of expanding and then simplifying [tex]\( 4(2 - p - q) + 3(4 + p - 2q) \)[/tex] is:
[tex]\[ 20 - p - 10q \][/tex]
