fully simplify 7r squared + 4 + 2r squared + 1

To simplify the expression \( 7r^2 + 4 + 2r^2 + 1 \), we need to combine like terms. 

1. Combine the \( r^2 \) terms:
   \[
   7r^2 + 2r^2 = 9r^2
   \]

2. Next, combine the constant terms:
   \[
   4 + 1 = 5
   \]

3. Put these together:
   \[
   9r^2 + 5
   \]

Therefore, the fully simplified expression is:
\[
9r^2 + 5
\]

Would you like additional details or have any questions?

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Here are some related questions to consider:
1. How do you simplify expressions with multiple variables?
2. What are like terms, and why are they important in simplification?
3. How do coefficients affect the simplification of expressions?
4. What is the difference between simplifying and factoring an expression?
5. How can you check if an expression is fully simplified?

**Tip:** Always start by combining like terms when simplifying algebraic expressions!

Simplify the expression 7r^2 + 4 + 2r^2 + 1 by combining like terms. This problem demonstrates basic algebra concepts, including combining quadratic terms and constants, suitable for students in Grades 6-8.

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