Final answer:
In mathematics, terms refer to parts of an algebraic expression that are added or subtracted. Like terms have the same variables and can be combined, while coefficients are numerical multipliers of variables, and constant terms are numbers without variables. To simplify, combine like terms and check for reasonableness.
Step-by-step explanation:
To simplify algebraic expressions, you need to understand the terminology used. Firstly, terms are the individual parts of an equation or expression that are added or subtracted. Like terms are terms that have the same variables raised to the same powers, although they may have different coefficients. Coefficients are the numerical part of the terms that multiply the variable(s). Lastly, constant terms are numbers that do not contain variables.
Consider an expression like 3x + 2y - 5x + 8. The terms of this expression are 3x, 2y, -5x, and 8. The like terms here are 3x and -5x since they contain the same variable x. The coefficients are the numbers 3 and -5 that multiply the variable x, and 2 that multiplies the variable y. The number 8 is a constant term because it does not have a variable associated with it.
When simplifying expressions, you would combine like terms, here 3x and -5x can be combined to -2x. So, the simplified expression is -2x + 2y + 8. To check if your answer is reasonable, ensure that you have combined all like terms and that the expression is in its simplest form.