Final answer:
A constant is a term with only a number part, while like terms have the same variable parts and can be combined in algebraic expressions. Every term must have the same dimensions to be added or subtracted, which is why only like terms with the same variables can be combined.
Step-by-step explanation:
A constant is a term with a number part but no variable. Like terms are terms that have the same variable parts. When working with algebraic expressions, it's important to recognize like terms as they can be combined through addition or subtraction. For instance, if the variable x is the independent variable and y is the dependent variable, you would typically choose a value to substitute for x and then solve for y.
It's essential to remember that every term in an expression must have the same dimensions; this is the principle that prevents us from combining terms with different variable parts, like adding apples and oranges. In an equation, the expressions on each side must balance, meaning they have the same dimensions. This is also why two terms must have the same variable parts to be considered like terms and thus can be combined. As an example, consider the equation of a line where x and y are the variables, and b and m represent constants in the equation y = mx + b. To understand how this works, let's look at a numerical example where x is given a value, and we solve for y based on that.