To simplify the given expression [tex]\( -7a^2b^2 - 4a^2b^2 + 9a^2b^2 - a^2b^2 \)[/tex], we combine the like terms. Here’s a step-by-step solution:
1. Identify Like Terms:
All the terms in the expression [tex]\( -7a^2b^2, -4a^2b^2, 9a^2b^2, \)[/tex] and [tex]\( -a^2b^2 \)[/tex] are like terms because each term contains the same variable parts [tex]\( a^2b^2 \)[/tex].
2. Combine Coefficients:
Since the terms are like terms, you can combine their coefficients:
[tex]\[
-7 + (-4) + 9 + (-1)
\][/tex]
3. Calculate the Sum of Coefficients:
[tex]\[
-7 - 4 + 9 - 1
\][/tex]
4. Perform the Arithmetic:
- First, combine [tex]\(-7\)[/tex] and [tex]\(-4\)[/tex]:
[tex]\[
-7 - 4 = -11
\][/tex]
- Then, add [tex]\(9\)[/tex]:
[tex]\[
-11 + 9 = -2
\][/tex]
- Finally, subtract [tex]\(1\)[/tex]:
[tex]\[
-2 - 1 = -3
\][/tex]
5. Write the Simplified Expression:
The simplified expression, combining the coefficients with the variable part [tex]\(a^2b^2\)[/tex], is:
[tex]\[
-3a^2b^2
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
-3a^2b^2
\][/tex]
