(k^3-7k+2)-(k^2-12)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression (k^3 - 7k + 2) - (k^2 - 12)

This article will guide you through simplifying the expression (k^3 - 7k + 2) - (k^2 - 12). We will break down the process step-by-step and explain the concepts involved.

Understanding the Expression

The expression involves subtracting two polynomials:

• (k^3 - 7k + 2): This is a polynomial with three terms.
• (k^2 - 12): This is a polynomial with two terms.

Simplifying the Expression

1. Distribute the negative sign: Remember that subtracting a polynomial is the same as adding its opposite. Therefore, we distribute the negative sign to each term within the second parenthesis:

   (k^3 - 7k + 2) + (-k^2 + 12)

2. Combine like terms: Now, we group terms with the same variable and exponent together.

   k^3 - k^2 - 7k + 12 + 2

3. Simplify: Finally, we combine the constant terms.

   k^3 - k^2 - 7k + 14

Final Result

Therefore, the simplified form of the expression (k^3 - 7k + 2) - (k^2 - 12) is k^3 - k^2 - 7k + 14.

Key Points

• Distribution: Remember to distribute the negative sign when subtracting polynomials.
• Combining Like Terms: Group terms with the same variable and exponent for simplification.
• Order of Operations: Follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.