Final answer:
The simplified form of expression (a) is 6a²b, which is obtained by adding and subtracting like terms. For expression (b), the simplified form is 5a²b + 4ab², where we combine like terms for a²b and leave the term with ab² as it is because it does not share the same exponent on both variables.
Step-by-step explanation:
To simplify the given expressions, we'll combine like terms. Like terms in algebra are terms that have the same variable raised to the same power.
Expression (a)
3a²b + 4a²b - a²b
First, we identify the like terms. Here, all the terms are like terms because they all have the term a²b. To simplify, we add or subtract the coefficients (the numerical parts) of these terms.
3a²b + 4a²b equals 7a²b, and subtracting a²b from 7a²b gives us 6a²b.
Therefore, the simplified form of expression (a) is 6a²b.
Expression (b)
3a²b + 4ab² + 2a²b
We have two like terms: 3a²b and 2a²b. These can be combined. However, 4ab² is not a like term with 3a²b and 2a²b because the exponent on b is different.
Adding 3a²b and 2a²b gives us 5a²b. Since 4ab² does not combine with the other terms, it remains as is.
Therefore, the simplified form of expression (b) is 5a²b + 4ab².