Let's simplify the given expression step-by-step:
The given expression is:
[tex]\[ 3ab^2 - 2a^2b + 5ab^2 - ab - a^2b + 2ab^2 + 2ab + 3a - b \][/tex]
Step 1: Combine like terms involving [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
1. Combine all terms involving [tex]\(ab^2\)[/tex]:
[tex]\[ 3ab^2 + 5ab^2 + 2ab^2 = 10ab^2 \][/tex]
2. Combine all terms involving [tex]\(-a^2b\)[/tex]:
[tex]\[ -2a^2b - a^2b = -3a^2b \][/tex]
3. Combine all terms involving [tex]\(ab\)[/tex]:
[tex]\[ -ab + 2ab = ab \][/tex]
4. Combine all terms involving [tex]\(a\)[/tex]:
[tex]\[ 3a \][/tex]
5. Combine the term involving [tex]\(-b\)[/tex]:
[tex]\[ -b \][/tex]
Step 2: Write down the simplified expression by combining the results of the like terms.
[tex]\[ 10ab^2 - 3a^2b + ab + 3a - b \][/tex]
Thus, the simplified expression is:
[tex]\[ -3a^2b + 10ab^2 + ab + 3a - b \][/tex]
