In simplifying expressions, how should terms with the same variable be treated?

• A. They should be multiplied together
• B. They should be added or subtracted based on their signs
• C. They should be ignored
• D. They should be split into separate equations

Answer: (B)

When simplifying expressions, terms with the same variable should be added or subtracted based on their signs. This is because like terms—terms that contain the same variable(s) raised to the same power—represent quantities that can be combined.

For example, if you have the expression (3x + 5x), both terms contain the variable (x). Since they are like terms, they can be added together to give (8x). Similarly, if you have (3x - 2x), you can subtract the coefficients, resulting in (1x) or simply (x).

This process of combining like terms helps in simplifying expressions to their most compact form, making it easier to understand and work with them. Ignoring these terms or treating them inappropriately, like multiplying or splitting them into separate equations, would lead to incorrect results and loss of valuable information in the equation.