Which of the following is true about like terms?

Which of the following is true about like terms?

• A. They must have the same coefficient.
• B. They must have the same variable and exponent.
• C. They can have different numerical coefficients.
• D. They must be constants.

Answer: (B)

The correct answer highlights an essential principle of algebra: like terms share the same variable and exponent. This means that in the expression \( 3x^2 \) and \( 5x^2 \), both terms are considered like terms because they contain the same variable \( x \) raised to the exponent \( 2 \). When terms are like, they can be combined through addition or subtraction. Combining terms that meet this criterion simplifies the expression effectively. For example, \( 3x^2 + 5x^2 \) simplifies to \( 8x^2 \). Although some options might suggest other characteristics of like terms, they do not accurately define what makes terms like. It's crucial to understand that differing coefficients do not prevent terms from being like terms; rather, those coefficients can be summed or subtracted. Moreover, like terms are not restricted to being constants; they can involve variables as well. Thus, the main takeaway is that what defines like terms is having the same variable and exponent, enabling their combination in algebraic expressions.

The correct answer highlights an essential principle of algebra: like terms share the same variable and exponent. This means that in the expression ( 3x^2 ) and ( 5x^2 ), both terms are considered like terms because they contain the same variable ( x ) raised to the exponent ( 2 ).

When terms are like, they can be combined through addition or subtraction. Combining terms that meet this criterion simplifies the expression effectively. For example, ( 3x^2 + 5x^2 ) simplifies to ( 8x^2 ).

Although some options might suggest other characteristics of like terms, they do not accurately define what makes terms like. It's crucial to understand that differing coefficients do not prevent terms from being like terms; rather, those coefficients can be summed or subtracted. Moreover, like terms are not restricted to being constants; they can involve variables as well. Thus, the main takeaway is that what defines like terms is having the same variable and exponent, enabling their combination in algebraic expressions.