Question

which expression is equivalent to \\((9 + 4m + m^2) + (-4m^2 + 9 + 4m)\\)\\(-3m^2 - 8m + 18\\)\\(3m^2 - 8m - 18\\)\\(-3m^2 + 8m - 18\\)\\(-3m^2 + 8m + 18\\)

Explanation:

Step1: Expand the expression

First, we have the expression \((9 + 4m + m^2)+(-4m^2 + 9 + 4m)\). We need to remove the parentheses:
\(9 + 4m + m^2-4m^2 + 9 + 4m\)

Step2: Combine like terms

• For the \(m^2\) terms: \(m^2-4m^2=-3m^2\)
• For the \(m\) terms: \(4m + 4m = 8m\)
• For the constant terms: \(9 + 9=18\)

Combining these results, we get \(-3m^2 + 8m + 18\)

Answer:

\(-3m^2 + 8m + 18\) (corresponding to the last option in the given choices)