Question

which of the following are terms in this expression? select all that apply.
$k^3 - k^2 - m^2$
$-k^3$
$k$
$-m^2$
$9k^3$

Explanation:

Step1: Analyze the expression \(k^{3}-k^{2}-m^{2}\)

The terms of an algebraic expression are the parts separated by addition or subtraction signs. So the terms in \(k^{3}-k^{2}-m^{2}\) are \(k^{3}\), \(-k^{2}\), and \(-m^{2}\).

Step2: Evaluate each option

• For \(-k^{3}\): The original expression has \(k^{3}\), not \(-k^{3}\), so this is not a term.
• For \(k\): The original expression has \(k^{3}\) and \(k^{2}\), not \(k\), so this is not a term.
• For \(-m^{2}\): This is exactly one of the terms in the expression \(k^{3}-k^{2}-m^{2}\) (since the expression can be thought of as \(k^{3}+(-k^{2})+(-m^{2})\)).
• For \(9k^{3}\): The original expression has \(k^{3}\), not \(9k^{3}\), so this is not a term.

Answer:

The only correct term among the options is \(-m^{2}\). So the correct option is the one with \(-m^{2}\) (the third option in the given choices).