Let's solve the expression:

\[
(x^2 + 3x + 7) - (-6x^2 - 2x + 5)
\]

To simplify:

1. Distribute the negative sign across the second expression:

\[
= x^2 + 3x + 7 + 6x^2 + 2x - 5
\]

2. Now, combine like terms:

- Combine the \(x^2\) terms: \(x^2 + 6x^2 = 7x^2\)
- Combine the \(x\) terms: \(3x + 2x = 5x\)
- Combine the constants: \(7 - 5 = 2\)

The simplified expression is:

\[
7x^2 + 5x + 2
\]

Let me know if you'd like further details or have any questions!

Here are five related questions for practice:
1. Simplify \( (2x^2 - 4x + 3) - (x^2 + 5x - 1) \).
2. Solve \( (3x + 7) - (2x + 5) \).
3. Factor the expression \( 7x^2 + 5x + 2 \).
4. Simplify \( (5x^2 - 2x + 8) + (3x^2 + 4x - 6) \).
5. Combine like terms in \( 9x^2 + 3x + 6 - 4x^2 + 5x - 2 \).

**Tip:** Always distribute negative signs carefully to avoid sign errors in algebraic expressions.

Learn how to simplify the polynomial expression (x² + 3x + 7) - (-6x² - 2x + 5) by distributing negative signs and combining like terms. This step-by-step solution is ideal for students in Grades 8-10 who are mastering algebraic expressions and polynomials.

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