---(4x3---5x2-%2B-3x).jpeg "(3x3 - 2x2 - 6x) - (4x3 - 5x2 + 3x)")
Simplifying Algebraic Expressions: (3x³ - 2x² - 6x) - (4x³ - 5x² + 3x)
This article will guide you through simplifying the algebraic expression: (3x³ - 2x² - 6x) - (4x³ - 5x² + 3x).
Understanding the Problem
The expression involves subtracting one polynomial from another. Both polynomials have terms with varying powers of 'x'. To simplify it, we need to combine like terms.
Steps to Simplify
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Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1. This gives us: 3x³ - 2x² - 6x - 4x³ + 5x² - 3x
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Combine like terms: Identify terms with the same power of 'x' and combine their coefficients:
- x³ terms: 3x³ - 4x³ = -x³
- x² terms: -2x² + 5x² = 3x²
- x terms: -6x - 3x = -9x
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Write the simplified expression: Combining all the simplified terms, we get the simplified expression: -x³ + 3x² - 9x
Conclusion
Therefore, the simplified form of the expression (3x³ - 2x² - 6x) - (4x³ - 5x² + 3x) is -x³ + 3x² - 9x. This process of combining like terms is a fundamental step in simplifying and solving algebraic expressions.