Simplifying the Expression: (8x^26x3)(4x^25x+4)
This article will guide you through the process of simplifying the expression (8x^26x3)(4x^25x+4).
Understanding the Problem
We are given a subtraction problem involving two polynomials. The goal is to simplify this expression by combining like terms.
StepbyStep Solution

Distribute the negative sign: Since we are subtracting the entire second polynomial, we need to distribute the negative sign. This means changing the sign of each term inside the second parentheses:
(8x^2  6x  3) + (4x^2 + 5x  4)

Combine like terms: Now, identify and group terms with the same variable and exponent:
(8x^2  4x^2) + (6x + 5x) + (3  4)

Simplify: Perform the indicated operations for each group:
4x^2  x  7
Final Result
The simplified form of the expression (8x^26x3)(4x^25x+4) is 4x^2  x  7.
Key Points
 Distributing the negative sign: Remember to change the sign of all terms within the second parenthesis.
 Combining like terms: Only terms with the same variable and exponent can be added or subtracted together.
 Simplifying: Perform the necessary operations to get the final, simplified expression.
By following these steps, you can confidently simplify polynomial expressions involving subtraction.