https://file.aiquickdraw.com/mathbot/file/1726104822861y5p71bea.jpg

The expression in the image is:

\[
10x^2 + 13x - 3 - (5x - 1)
\]

Let me simplify this expression step-by-step:

1. Distribute the negative sign across the terms inside the parentheses:
   \[
   10x^2 + 13x - 3 - 5x + 1
   \]

2. Combine like terms:
   \[
   10x^2 + (13x - 5x) + (-3 + 1) = 10x^2 + 8x - 2
   \]

Thus, the simplified expression is:

\[
10x^2 + 8x - 2
\]

Would you like further details on how to solve, factor, or analyze this expression?

Here are some related questions to expand on this concept:
1. How do you factor quadratic expressions like \(10x^2 + 8x - 2\)?
2. Can this quadratic expression be solved for its roots using the quadratic formula?
3. How would you find the vertex of the quadratic equation \(10x^2 + 8x - 2 = 0\)?
4. What is the importance of completing the square when dealing with quadratic expressions?
5. How does this quadratic expression graph as a parabola?

**Tip**: Always combine like terms carefully, especially when dealing with subtraction and parentheses!

Learn how to simplify the polynomial expression 10x^2 + 13x - 3 - (5x - 1) with detailed steps. This algebraic problem covers polynomial simplification and distributive property. Suitable for students in Grades 9-10.

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