Simplifying Polynomial Expressions: (5x^3  3x + 6)  (2x^2  4x + 8)
This article will guide you through the process of simplifying the given polynomial expression: (5x^3  3x + 6)  (2x^2  4x + 8).
Understanding the Problem
We are dealing with two polynomials, each consisting of several terms. To simplify the expression, we need to subtract the second polynomial from the first.
The Steps to Simplification

Distribute the negative sign: The minus sign in front of the second polynomial means we multiply each term inside the parentheses by 1.
(5x^3  3x + 6) + (1)(2x^2  4x + 8)

Simplify: Multiply the 1 into the second polynomial:
(5x^3  3x + 6)  2x^2 + 4x  8

Combine like terms: Identify terms with the same variable and exponent (like terms) and combine their coefficients.
5x^3  2x^2  3x + 4x + 6  8

Final simplification: Combine the coefficients of like terms:
5x^3  2x^2 + x  2
The Result
The simplified form of the polynomial expression (5x^3  3x + 6)  (2x^2  4x + 8) is 5x^3  2x^2 + x  2.
Key Takeaways
 Distribute the negative sign: Always remember to distribute the negative sign when subtracting polynomials.
 Combine like terms: Grouping similar terms together is crucial for simplification.
 Understanding exponents: Pay close attention to the exponents of variables when combining like terms.
By following these steps, you can effectively simplify any polynomial expression involving subtraction.