%E2%88%92(%E2%88%92x2%E2%88%929x%2B6).jpeg "(−x2−3x+3)−(−x2−9x+6)")
Simplifying Algebraic Expressions: (−x2−3x+3)−(−x2−9x+6)
This article will walk you through the process of simplifying the algebraic expression: (−x2−3x+3)−(−x2−9x+6).
Understanding the Problem
We are given two polynomials enclosed in parentheses. The expression involves subtraction between these polynomials. Our goal is to simplify the expression by removing the parentheses and combining like terms.
Step-by-Step Solution
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Distribute the negative sign: The minus sign in front of the second set of parentheses acts as a multiplier of -1. Therefore, we distribute this -1 to each term inside the second set of parentheses.
(-x2 - 3x + 3) + (x2 + 9x - 6)
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Combine like terms: We identify terms with the same variable and exponent and combine their coefficients.
- x2 terms: -x2 + x2 = 0
- x terms: -3x + 9x = 6x
- Constant terms: 3 - 6 = -3
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Simplified expression: After combining like terms, we are left with: 6x - 3
Conclusion
The simplified form of the expression (−x2−3x+3)−(−x2−9x+6) is 6x - 3. By understanding the rules of distributing negative signs and combining like terms, we can effectively simplify complex algebraic expressions.