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
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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)
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Combine like terms: Now, we group terms with the same variable and exponent together.
k^3 - k^2 - 7k + 12 + 2
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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.