Math Problem Statement

solve this and provide the right answers

Simplify the following expression: 8x^2 - 10x + 6 - 9x - 12x^2

Solution

The given expression is:

8x210x+69x12x28x^2 - 10x + 6 - 9x - 12x^2

Steps to simplify:

  1. Group like terms:

    • Combine x2x^2-terms: 8x212x28x^2 - 12x^2.
    • Combine xx-terms: 10x9x-10x - 9x.
    • Constant term: 66.
  2. Simplify each group:

    • 8x212x2=4x28x^2 - 12x^2 = -4x^2.
    • 10x9x=19x-10x - 9x = -19x.
    • Constant term remains 66.
  3. Write the simplified expression: 4x219x+6-4x^2 - 19x + 6

Final Answer:

4x219x+6-4x^2 - 19x + 6

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


Here are 5 related questions for practice:

  1. How do you combine terms in an expression like 5x2+3x42x2+x5x^2 + 3x - 4 - 2x^2 + x?
  2. What is the standard form of a quadratic expression?
  3. Can you identify the coefficient of x2x^2 in the simplified expression above?
  4. How do you determine the degree of a polynomial like 3x34x+13x^3 - 4x + 1?
  5. What is the significance of the constant term in a polynomial?

Tip: Always organize like terms by their degrees to avoid mistakes in simplification.

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Simplification

Formulas

Combining like terms in a polynomial

Theorems

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Suitable Grade Level

Grades 8-10