Question

greg says that the expression xyz has three terms because it uses three different variables. explain whether he is correct.
choose the correct answer below.
a. greg is not correct. the expression xyz has no terms because there are no plus or minus signs.
b. greg is not correct. the expression xyz has one term, xyz. it is the only term because there are no other parts separated by a plus or minus sign.
c. greg is correct. every variable in an expression is a term. this means that x, y, and z are the three terms of the expression xyz.
d. greg is correct but his reasoning is incorrect. the three terms are x, y, and z because they are actually separated by multiplication, even though the multiplication symbol is not shown.

Explanation:

Step1: Understand the definition of a term

A term in an algebraic expression is a single number, variable, or the product of numbers and variables. Terms are separated by \(+\) or \(-\) signs.

Step2: Analyze the expression \(xyz\)

The expression \(xyz\) is a product of variables \(x\), \(y\), and \(z\). Since there are no \(+\) or \(-\) signs in the expression \(xyz\), it is a single - term expression.

Step3: Evaluate each option

• Option A: The statement “The expression \(xyz\) has no terms because there are no plus or minus signs” is incorrect. Just because there are no \(+\) or \(-\) signs does not mean there are no terms. In fact, \(xyz\) is a single term.
• Option B: The statement “Greg is not correct. The expression \(xyz\) has one term. \(xyz\) is the only term because there are no other parts separated by a plus or minus sign” is correct. As per the definition of a term (a single entity in an algebraic expression, which can be a product of variables), \(xyz\) is a single term.
• Option C: The statement “Greg is correct. Every variable in an expression is a term. This means that \(x\), \(y\), and \(z\) are the three terms of the expression \(xyz\)” is incorrect. In the expression \(xyz\) (where it is \(x\times y\times z\)), it is a single - term (a product of variables), not three separate terms. Variables \(x\), \(y\), \(z\) are factors of the single term \(xyz\).
• Option D: The statement “Greg is correct but his reasoning is incorrect. The three terms are \(x\), \(y\), and \(z\) because they are actually separated by multiplication, even though the multiplication symbol is not shown” is incorrect. Multiplication does not separate terms. Terms are separated by \(+\) or \(-\) signs. And \(xyz\) is a single term.

Answer:

B. Greg is not correct. The expression \(xyz\) has one term. \(xyz\) is the only term because there are no other parts separated by a plus or minus sign.