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Simplify: [tex]-1(8c + 9d) + 2(11c - 6d)[/tex].

A. [tex]-7cd[/tex]
B. [tex]14c - 21d[/tex]
C. [tex]-17c - 10d[/tex]
D. [tex]-8c - 9d + 22c - 12d[/tex]

Answer :

Sure! Let's simplify the expression step-by-step:

We start with the expression:
[tex]\[ -1(8c + 9d) + 2(11c - 6d) \][/tex]

### Step 1: Distribute the Constants
First, we need to distribute [tex]\(-1\)[/tex] and [tex]\(2\)[/tex] into the parentheses.

For [tex]\(-1(8c + 9d)\)[/tex]:
[tex]\[ -1 \cdot 8c = -8c \][/tex]
[tex]\[ -1 \cdot 9d = -9d \][/tex]
So,
[tex]\[ -1(8c + 9d) = -8c - 9d \][/tex]

For [tex]\(2(11c - 6d)\)[/tex]:
[tex]\[ 2 \cdot 11c = 22c \][/tex]
[tex]\[ 2 \cdot -6d = -12d \][/tex]
So,
[tex]\[ 2(11c - 6d) = 22c - 12d \][/tex]

Now, our expression looks like:
[tex]\[ -8c - 9d + 22c - 12d \][/tex]

### Step 2: Combine Like Terms
Next, we combine the [tex]\(c\)[/tex] terms and the [tex]\(d\)[/tex] terms separately.

For the [tex]\(c\)[/tex] terms:
[tex]\[ -8c + 22c = (22 - 8)c = 14c \][/tex]

For the [tex]\(d\)[/tex] terms:
[tex]\[ -9d - 12d = (-9 - 12)d = -21d \][/tex]

### Step 3: Write the Final Simplified Expression
Combining the results, we get:
[tex]\[ 14c - 21d \][/tex]

So, the simplified expression is
[tex]\[ \boxed{14c - 21d} \][/tex]

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Rewritten by : Barada