(2k^3-7k^2+3k)-(-4k^2+5k)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (2k³ - 7k² + 3k) - (-4k² + 5k)

This article will guide you through the process of simplifying the algebraic expression: (2k³ - 7k² + 3k) - (-4k² + 5k).

Understanding the Problem

The expression involves:

• Variables: 'k' representing an unknown value.
• Coefficients: Numbers multiplied by the variables (2, -7, 3, -4, 5).
• Exponents: Powers of the variables (³ and ²).
• Parentheses: Indicating the order of operations and grouping terms.

Simplifying the Expression

1. Distribute the negative sign:

   • The minus sign in front of the second parenthesis means we multiply each term inside it by -1.
   • This gives us: (2k³ - 7k² + 3k) + 4k² - 5k

2. Combine like terms:

   • We combine terms with the same variable and exponent.
   • k³ terms: There's only one k³ term: 2k³
   • k² terms: -7k² + 4k² = -3k²
   • k terms: 3k - 5k = -2k

3. Write the simplified expression:

   • Putting all the combined terms together, we get: 2k³ - 3k² - 2k

Conclusion

By applying the principles of distributing negative signs and combining like terms, we successfully simplified the expression (2k³ - 7k² + 3k) - (-4k² + 5k) to 2k³ - 3k² - 2k. This is the simplified form of the original expression, representing the same value for any value of 'k'.