%2B(-2x%5E3-x%5E2%2B6x).jpeg "(4x^3-5x^2+3x)+(-2x^3-x^2+6x)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
In mathematics, polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Simplifying polynomials involves combining like terms to create a more concise expression. Let's explore how to simplify the polynomial expression: (4x³ - 5x² + 3x) + (-2x³ - x² + 6x)
Understanding the Steps
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Identify Like Terms: Look for terms with the same variable and exponent. In this case, we have:
- x³ terms: 4x³ and -2x³
- x² terms: -5x² and -x²
- x terms: 3x and 6x
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Combine Like Terms: Add or subtract the coefficients of like terms.
- x³ terms: 4x³ - 2x³ = 2x³
- x² terms: -5x² - x² = -6x²
- x terms: 3x + 6x = 9x
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Write the Simplified Expression: Combine the simplified terms to get the final expression: 2x³ - 6x² + 9x
Summary
Simplifying the polynomial expression (4x³ - 5x² + 3x) + (-2x³ - x² + 6x) results in 2x³ - 6x² + 9x. By combining like terms, we have successfully simplified the expression into a more concise and manageable form. This process of identifying and combining like terms is a fundamental concept in algebra and forms the basis for solving many mathematical problems.