To solve the expression \( a(-a) + 1 \):

1. First, simplify the product \( a(-a) \):
   \[
   a \cdot (-a) = -a^2
   \]

2. Next, add 1 to the result:
   \[
   -a^2 + 1
   \]

So, the simplified expression is:
\[
-a^2 + 1
\]

Would you like any further details or have any questions about this solution?

Here are some related questions to further explore this topic:

1. How do you solve for \( a \) if given an equation like \( a(-a) + 1 = 0 \)?
2. What are the properties of exponents when multiplying variables?
3. How do you handle negative coefficients in algebraic expressions?
4. Can you graph the function \( f(a) = -a^2 + 1 \) and describe its properties?
5. What is the vertex of the parabola \( y = -a^2 + 1 \)?
6. How does the sign of the coefficient in front of \( a^2 \) affect the direction of the parabola?
7. What is the axis of symmetry for the parabola \( y = -a^2 + 1 \)?
8. How do you determine the maximum value of the quadratic function \( y = -a^2 + 1 \)?

**Tip:** When simplifying algebraic expressions, always handle the operations step-by-step, keeping track of positive and negative signs carefully.

Learn how to simplify the expression a(-a) + 1 with a detailed step-by-step solution. This problem covers key algebraic concepts, including negative coefficients and simplifying algebraic expressions. Suitable for students in Grades 9-12.

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