Question

simplify. ((2v^2 + 3v + 6)+(-4v^2 - 7v + 3)-(-2v^2 - 3v - 7))

Explanation:

Step1: Remove parentheses and distribute the negative sign

First, we remove the parentheses. For the third parentheses, we distribute the negative sign:
$$(2v^2 + 3v + 6)+(-4v^2 - 7v + 3)-(-2v^2 - 3v - 7)$$
$$= 2v^2 + 3v + 6 - 4v^2 - 7v + 3 + 2v^2 + 3v + 7$$

Step2: Combine like terms for \(v^2\) terms

Combine the \(v^2\) terms: \(2v^2 - 4v^2 + 2v^2\)
$$(2 - 4 + 2)v^2=0v^2$$

Step3: Combine like terms for \(v\) terms

Combine the \(v\) terms: \(3v - 7v + 3v\)
$$(3 - 7 + 3)v=-v$$

Step4: Combine constant terms

Combine the constant terms: \(6 + 3 + 7\)
$$6 + 3 + 7 = 16$$

Step5: Combine all results

Now, combine the results from the previous steps: \(0v^2 - v + 16\), which simplifies to \(-v + 16\)

Answer:

\(-v + 16\)