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(a) Expand and then simplify [tex]$4(2-p-q) + 3(4+p-2q)$[/tex].

Sagot :

GinnyAnsweridn
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]
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