Let's simplify the given expression:

\[
(X² + 3x + 7) - (-6x² - 2x + 5)
\]

Step-by-step solution:

1. Distribute the negative sign across the second set of parentheses:
   \[
   = X² + 3x + 7 + 6x² + 2x - 5
   \]

2. Combine like terms:
   - \(X² + 6X² = 7X²\)
   - \(3X + 2X = 5X\)
   - \(7 - 5 = 2\)

So the simplified expression is:

\[
7X² + 5X + 2
\]

Would you like further details or have any other questions?

Here are some related questions to explore:

1. How would you factor the expression \(7X² + 5X + 2\)?
2. What is the value of the expression for \(X = 2\)?
3. Can you solve \(7X² + 5X + 2 = 0\) using the quadratic formula?
4. How do we graph the quadratic equation \(y = 7X² + 5X + 2\)?
5. What is the discriminant of the quadratic equation \(7X² + 5X + 2\)?

**Tip:** Always check for like terms when simplifying expressions—it helps keep things organized!

Learn how to simplify the expression (X² + 3x + 7) - (-6x² - 2x + 5) with a detailed step-by-step solution. This problem covers essential algebraic concepts like the distributive property and combining like terms. Ideal for students in Grades 8-10.

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