Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the polynomial expression: (5x^3  x + 2x^2) + (7  4x)  (6x^2 + 5x^3  3)
Understanding the Steps
To simplify this expression, we will follow these steps:
 Remove parentheses: We will distribute any negative signs in front of parentheses.
 Combine like terms: We will group together terms with the same variable and exponent.
 Simplify: We will perform the necessary arithmetic operations.
Simplifying the Expression
Let's break down the simplification process step by step:

Removing parentheses:
 The first set of parentheses doesn't have a negative sign in front, so we can simply remove them.
 The second set of parentheses also doesn't have a negative sign in front.
 The third set of parentheses has a negative sign in front. We distribute this negative sign to each term inside the parentheses:
 (6x^2 + 5x^3  3) = 6x^2  5x^3 + 3

Combining like terms:
 x^3 terms: 5x^3  5x^3 = 0x^3 (these terms cancel out)
 x^2 terms: 2x^2  6x^2 = 4x^2
 x terms: x  4x = 5x
 Constant terms: 7 + 3 = 10

Simplifying:
Putting all the simplified terms together, we get:
0x^3  4x^2  5x + 10
Final Answer
Therefore, the simplified form of the given polynomial expression is 4x^2  5x + 10.