Explanation:

To solve this problem, we need to simplify the given expression by combining like terms.

Step 1: Identify the like terms

Like terms are those terms which have the same variables raised to the same power.

The like terms in the given expression are:

- 2ab2c2
- 4a2b
- -5a
- 2bc2

Step 2: Combine the like terms

To combine the like terms, we need to add or subtract the coefficients of the like terms.

- The coefficient of 2ab2c2 is -2.
- The coefficient of 4a2b is -4.
- The coefficient of -5a is -5.
- The coefficient of 2bc2 is 2.

Hence, the simplified expression becomes:

-10a + 2b - 2ab2c2 + 4ab2c2 + 2a2bc2 - 2bc2

Simplifying further,

-10a + 2b + 2a2bc2

is the final answer.

Points to Remember - Algebraic Expressions and Identities:

- An algebraic expression is a combination of variables, constants, and arithmetic operations.
- The like terms in an algebraic expression are those terms that have the same variables raised to the same power.
- To combine like terms, we add or subtract the coefficients of the like terms.
- An identity is an equation that is true for all values of the variables.
- The distributive property states that a(b + c) = ab + ac.
- The commutative property states that changing the order of the terms does not change the value of the expression.
- The associative property states that changing the grouping of the terms does not change the value of the expression.