Math Problem Statement

(−x 2 −4x+1)−(2x 2 +9)

Solution

The expression is:

(x24x+1)(2x2+9)-(x^2 - 4x + 1) - (2x^2 + 9)

Let's simplify it step by step.

  1. First, distribute the negative signs: x2+4x12x29-x^2 + 4x - 1 - 2x^2 - 9

  2. Combine like terms:

    • The x2x^2 terms: x22x2=3x2-x^2 - 2x^2 = -3x^2
    • The constant terms: 19=10-1 - 9 = -10

So, the simplified expression is:

3x2+4x10-3x^2 + 4x - 10

Would you like further details or clarifications?

Here are some related questions:

  1. How would you factor a quadratic expression like this one?
  2. Can you solve 3x2+4x10=0-3x^2 + 4x - 10 = 0?
  3. What is the vertex of the quadratic function 3x2+4x10-3x^2 + 4x - 10?
  4. How do you find the axis of symmetry for a quadratic equation?
  5. What are the properties of parabolas when the coefficient of x2x^2 is negative?

Tip: When combining like terms, always ensure you are working with the same variable or constant values to avoid mistakes.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Polynomials
Combining Like Terms

Formulas

Distributive Property a(b + c) = ab + ac

Theorems

None specifically required for simplification, though combining like terms and the distributive property are key.

Suitable Grade Level

Grades 8-10