Question

which of the following are terms in this expression? select all that apply.
$5t^2v - 9 - tv^2$
$5t^2v$ $-tv^2$ $-t$ $v^2$

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.

Step2: Analyze the given expression \(5t^{2}v - 9 - tv^{2}\)

• The first term is \(5t^{2}v\) (product of \(5\), \(t^{2}\), and \(v\)).
• The second term is \(-9\) (a single number).
• The third term is \(-tv^{2}\) (product of \(- 1\), \(t\), and \(v^{2}\)).
• The options \(-t\) and \(v^{2}\) are not present as terms in the expression. The \(-t\) is not a separate term (the term with \(t\) is \(-tv^{2}\)) and \(v^{2}\) is part of the term \(-tv^{2}\) but not a separate term.

Answer:

The correct terms in the expression \(5t^{2}v - 9 - tv^{2}\) are \(5t^{2}v\) and \(-tv^{2}\) and \(- 9\) (the \(-t\) and \(v^{2}\) are incorrect selections). So the correct checked options should be \(5t^{2}v\), \(-tv^{2}\) and the term \(-9\) (if there was an option for \(-9\), but from the given options with the current checkmarks, the wrong ones are \(-t\) and \(v^{2}\)). To correct, the terms of the expression \(5t^{2}v - 9 - tv^{2}\) are separated by the addition/subtraction operations. So the terms are \(5t^{2}v\), \(-9\), and \(-tv^{2}\). So among the given options, the correct ones are \(5t^{2}v\) (correctly checked), \(-tv^{2}\) (correctly checked), and the \(-9\) is a term but not in the given options with checkmarks here. The \(-t\) and \(v^{2}\) are not terms of the expression.