Solve for the sum of 2x^2 + 4x -3 and 6x^2 -2x +9

To find the sum of the two expressions \(2x^2 + 4x - 3\) and \(6x^2 - 2x + 9\), we add the corresponding terms:

1. **Combine the \(x^2\) terms:**
   \[
   2x^2 + 6x^2 = 8x^2
   \]

2. **Combine the \(x\) terms:**
   \[
   4x - 2x = 2x
   \]

3. **Combine the constant terms:**
   \[
   -3 + 9 = 6
   \]

Now, summing everything up, we get:
\[
8x^2 + 2x + 6
\]

Thus, the sum of the two expressions is \(8x^2 + 2x + 6\).

Would you like more details or have any questions?

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Here are some related questions:
1. How do you simplify algebraic expressions with more terms?
2. Can you solve for \(x\) in \(8x^2 + 2x + 6 = 0\)?
3. How do you factor quadratic expressions like \(2x^2 + 4x - 3\)?
4. What is the importance of combining like terms in algebra?
5. How do we solve systems of equations involving quadratics?

**Tip:** Always group similar terms (like powers of \(x\)) to simplify expressions efficiently!

Learn how to solve the sum of two polynomial expressions: 2x^2 + 4x - 3 and 6x^2 - 2x + 9. This solution demonstrates the process of combining like terms step-by-step, a key concept in algebra. Suitable for students in Grades 7-9.

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