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 stepbystep 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

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)

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

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.