Question

which of the following are terms in this expression? select all that apply.
$6m^2 + 5m^3$
options: 5, $5m^3$, $8m^3$, 6

Explanation:

1. A term in an algebraic expression is a single mathematical expression that is part of a sum or difference. In \(6m^{2}+5m^{3}\), the terms are \(6m^{2}\) and \(5m^{3}\).
2. Analyzing the options:

• \(5\): It is the coefficient of \(5m^{3}\), not a term on its own in this expression.
• \(5m^{3}\): This matches one of the terms in \(6m^{2}+5m^{3}\), so it is a term.
• \(8m^{3}\): This term is not present in the given expression \(6m^{2}+5m^{3}\).
• \(6\): It is the coefficient of \(6m^{2}\), not a term on its own in this expression.

Answer:

The correct terms in the expression \(6m^{2}+5m^{3}\) are \(5m^{3}\) (and also \(6m^{2}\) which is not among the given options to check, but among the provided options, only \(5m^{3}\) is a term of the expression. The other selected options: \(5\) is not a term (the coefficient is \(5\) for \(5m^{3}\), but \(5\) alone isn't a term here), \(8m^{3}\) is not in the expression, \(6\) is the coefficient of \(6m^{2}\) and not a term by itself in the way the options are presented. So the only correct selected option should be \(5m^{3}\), and the incorrect selections are \(5\), \(8m^{3}\), \(6\). So to correct, the answer is \(5m^{3}\) (the option with \(5m^{3}\) is the only correct one among the given choices for being a term of \(6m^{2}+5m^{3}\)).