Question

which of the following are terms in this expression? select all that apply.
$9u^3 + 1 + 2s^3t^3 + 10t^3$
$9u^2$ $2s^3$ $10t^3$ $1$

Explanation:

Step 1: 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 plus or minus signs.

Step 2: Analyze each option against the given expression \(9u^{3}+1 + 2s^{3}t^{3}+10t^{3}\)

• For \(9u^{2}\): The term in the expression is \(9u^{3}\), so \(9u^{2}\) is not a term of the given expression.
• For \(2s^{3}\): The term in the expression is \(2s^{3}t^{3}\), so \(2s^{3}\) is not a term of the given expression.
• For \(10t^{3}\): This term is present in the expression \(9u^{3}+1 + 2s^{3}t^{3}+10t^{3}\), so it is a valid term.
• For \(1\): This term is present in the expression \(9u^{3}+1 + 2s^{3}t^{3}+10t^{3}\), so it is a valid term.

Answer:

The correct terms in the expression \(9u^{3}+1 + 2s^{3}t^{3}+10t^{3}\) are \(1\), \(10t^{3}\). The terms \(9u^{2}\) and \(2s^{3}\) are incorrect. The correct terms should be identified as follows:

• The original expression has terms separated by plus signs. The terms are \(9u^{3}\), \(1\), \(2s^{3}t^{3}\), \(10t^{3}\). So among the given options:
• \(9u^{2}\) is incorrect (the exponent of \(u\) in the original term is \(3\), not \(2\)).
• \(2s^{3}\) is incorrect (the original term is \(2s^{3}t^{3}\), not \(2s^{3}\)).
• \(10t^{3}\) is a correct term as it appears in the expression.
• \(1\) is a correct term as it appears in the expression.

So the correct selected terms should be \(10t^{3}\) and \(1\), and the incorrect ones are \(9u^{2}\) and \(2s^{3}\). If we are to select the correct ones from the given check - marked options, we should un - check \(9u^{2}\) and \(2s^{3}\) and keep \(10t^{3}\) and \(1\) checked.