Question

greg says that the expression xyz has three terms because it uses three different variables. critique gregs reasoning and explain whether he is correct.
choose the correct answer below
o a. 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 symbols are not shown
o b. 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
o c. greg is not correct. the expression xyz has no terms because there are no plus or minus signs
o d. 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

Explanation:

In an algebraic expression, a term is a single number, variable, or the product of numbers and variables. The expression \(xyz\) is a single term because there are no plus or minus signs to separate it into multiple parts. Greg's reasoning in option A is incorrect as variables separated by multiplication (even if the multiplication symbol isn't shown) form a single term, not three separate terms. Option B is correct as every variable in an expression \(xyz\) (where there are no \(+\) or \(-\) signs) is part of the same single term. Option C is wrong because \(xyz\) does have a term (the whole \(xyz\) itself). Option D is wrong because \(xyz\) is one term, not because of the absence of other parts separated by \(+\) or \(-\) in the wrong sense (the key is the definition of a term as a product with no \(+\) or \(-\) to split it, and \(xyz\) fits the single - term definition).

Answer:

B. 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 \(xyz\)