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

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

Answer :

Sure! Let's simplify the expression step-by-step: [tex]\(-1(8c + 9d) + 2(11c - 6d)\)[/tex].

1. Distribute the numbers outside the parentheses:
- For [tex]\(-1(8c + 9d)\)[/tex]: Distribute [tex]\(-1\)[/tex] to both terms inside the parenthesis:
[tex]\[
-1 \times 8c = -8c \quad \text{and} \quad -1 \times 9d = -9d
\][/tex]
So, [tex]\(-1(8c + 9d) = -8c - 9d\)[/tex].

- For [tex]\(2(11c - 6d)\)[/tex]: Distribute [tex]\(2\)[/tex] to each term inside the parenthesis:
[tex]\[
2 \times 11c = 22c \quad \text{and} \quad 2 \times (-6d) = -12d
\][/tex]
So, [tex]\(2(11c - 6d) = 22c - 12d\)[/tex].

2. Combine all parts:
[tex]\[
-8c - 9d + 22c - 12d
\][/tex]

3. Combine like terms:
- Combine the [tex]\(c\)[/tex] terms: [tex]\(-8c + 22c = 14c\)[/tex].
- Combine the [tex]\(d\)[/tex] terms: [tex]\(-9d - 12d = -21d\)[/tex].

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

That's how you simplify the given expression!

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