Sure, let's break this problem down step by step to simplify the given expression:
The expression to simplify is:
[tex]\[
(9 - 4a^3b^3) - (-6a^3b^3 - 14 - a) - (-6a^3b^3 + 2a)
\][/tex]
### Step 1: Distribute the negative signs through the parentheses
First, distribute the negative signs to remove the parentheses:
[tex]\[
= 9 - 4a^3b^3 + 6a^3b^3 + 14 + a + 6a^3b^3 - 2a
\][/tex]
### Step 2: Combine like terms
Now, combine the like terms. Let's consider the terms involving [tex]\(a^3b^3\)[/tex], the constant terms, and the terms involving [tex]\(a\)[/tex]:
1. Combine the [tex]\(a^3b^3\)[/tex] terms:
[tex]\[
-4a^3b^3 + 6a^3b^3 + 6a^3b^3 = (6a^3b^3 + 6a^3b^3 - 4a^3b^3) = 8a^3b^3
\][/tex]
2. Combine the constant terms:
[tex]\[
9 + 14 = 23
\][/tex]
3. Combine the terms involving [tex]\(a\)[/tex]:
[tex]\[
a - 2a = -a
\][/tex]
### Step 3: Write the simplified expression
Putting all these simplified terms together, we get:
[tex]\[
8a^3b^3 - a + 23
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
8a^3b^3 - a + 23
\][/tex]
