Question

which of the following are terms in this expression? select all that apply.
$-7 - 3b^{2}$
$3$ $b^{2}$ $-6$ $-7$

Explanation:

Step1: Recall the definition of a term in an algebraic expression

A term in an algebraic expression is a single number, variable, or the product of numbers and variables, separated by addition or subtraction signs. For the expression \(-7 - 3b^{2}\), we can rewrite it as \(-7+(- 3b^{2})\) to clearly identify the terms.

Step2: Analyze each option

• For \(3\): The term with \(b^{2}\) is \(-3b^{2}\), not \(3\). So \(3\) is not a term.
• For \(b^{2}\): The term is \(-3b^{2}\), not \(b^{2}\) alone. So \(b^{2}\) is not a term.
• For \(-6\): The constant term in the expression is \(-7\), not \(-6\). So \(-6\) is not a term.
• For \(-7\): In the expression \(-7 - 3b^{2}\), \(-7\) is a constant term (a single number separated by the subtraction sign from \(-3b^{2}\)). So \(-7\) is a term. Also, when we consider the expression as a sum of terms: \(-7+(-3b^{2})\), the terms are \(-7\) and \(-3b^{2}\). Wait, maybe I made a mistake earlier. Let's re - express the original expression \(-7-3b^{2}\) as the sum of two terms: the first term is \(-7\) (a constant term) and the second term is \(-3b^{2}\) (a term with a variable). But let's check the options again. Wait, maybe the user's initial marking is wrong. Let's do it properly.

The expression \(-7 - 3b^{2}\) can be thought of as having two terms: \(-7\) (because it is a single number) and \(-3b^{2}\) (because it is the product of \(- 3\) and \(b^{2}\)). Now let's check each option:

• Option \(3\): The coefficient of \(b^{2}\) is \(-3\), not \(3\), so \(3\) is not a term.
• Option \(b^{2}\): The term is \(-3b^{2}\), so \(b^{2}\) alone is not a term.
• Option \(-6\): The constant term is \(-7\), not \(-6\), so \(-6\) is not a term.
• Option \(-7\): \(-7\) is a term in the expression \(-7 - 3b^{2}\) (since it is separated from \(-3b^{2}\) by the subtraction sign, and it is a single number).

Answer:

The only correct term among the given options is \(-7\). So the correct option is: \(-7\) (the box corresponding to \(-7\) should be checked, and the boxes for \(3\), \(b^{2}\), and \(-6\) should be unchecked)