(−8x2−5x+8)−(−6x2+3x−3)

2 min read Jun 17, 2024
(−8x2−5x+8)−(−6x2+3x−3)

Simplifying the Expression: (−8x2−5x+8)−(−6x2+3x−3)

This article will guide you through simplifying the given algebraic expression: (−8x2−5x+8)−(−6x2+3x−3).

Understanding the Problem

The expression involves subtraction of two polynomials. We need to simplify it by combining like terms.

Step-by-Step Solution

  1. Distribute the negative sign: The minus sign in front of the second set of parentheses changes the sign of each term inside it.

    (-8x^2 - 5x + 8) + (6x^2 - 3x + 3) 
    
  2. Combine like terms: Identify terms with the same variable and exponent and add their coefficients.

    (-8x^2 + 6x^2) + (-5x - 3x) + (8 + 3)
    
  3. Simplify: Combine the coefficients of the like terms.

    -2x^2 - 8x + 11 
    

Final Result

Therefore, the simplified form of the expression (−8x2−5x+8)−(−6x2+3x−3) is -2x^2 - 8x + 11.

Key Takeaways

  • Distribute negative signs: Remember to change the sign of each term within parentheses when a negative sign precedes them.
  • Combine like terms: Combine terms with the same variable and exponent by adding their coefficients.
  • Simplify: The result should be a simplified polynomial expression.

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