Question

combine like terms: 2m^2 + 5m - 3 + m^2 - 2m + 8

Explanation:

Step1: Identify like terms

The given expression is \(2m^2 + 5m - 3 + m^2 - 2m + 8\). The like terms for \(m^2\) are \(2m^2\) and \(m^2\); for \(m\) are \(5m\) and \(-2m\); and the constant terms are \(-3\) and \(8\).

Step2: Combine \(m^2\) terms

\(2m^2 + m^2=(2 + 1)m^2 = 3m^2\)

Step3: Combine \(m\) terms

\(5m-2m=(5 - 2)m = 3m\)

Step4: Combine constant terms

\(-3 + 8=5\)

Step5: Combine all results

Putting it all together, we get \(3m^2+3m + 5\) (Wait, let's re - check the constant term combination. \(-3+8 = 5\), the \(m\) terms: \(5m-2m = 3m\), and \(m^2\) terms: \(2m^2+m^2=3m^2\). So the combined expression is \(3m^2 + 3m+5\)? Wait, no, wait the original expression is \(2m^2 + 5m-3+m^2 - 2m + 8\). Let's do it again:

\(2m^2+m^2=3m^2\)

\(5m-2m = 3m\)

\(-3 + 8=5\)

So the combined expression is \(3m^2+3m + 5\)? Wait, but maybe I made a mistake. Wait, let's check the original problem again. The expression is \(2m^2 + 5m-3+m^2-2m + 8\). Let's group the terms:

\((2m^2+m^2)+(5m - 2m)+(-3 + 8)\)

\(=3m^2+3m + 5\)

Wait, but looking at the options (even though the options are a bit unclear), if we assume that maybe there was a typo and the constant term combination is \(-3 + 8=5\), \(m\) terms \(5m-2m = 3m\), \(m^2\) terms \(2m^2 + m^2=3m^2\). So the combined expression is \(3m^2+3m + 5\). But let's re - evaluate:

Wait, \(2m^2+m^2 = 3m^2\)

\(5m-2m=3m\)

\(-3 + 8 = 5\)

So the simplified expression is \(3m^2+3m + 5\)

Answer:

\(3m^2 + 3m+5\)