Simplifying Polynomial Expressions: A StepbyStep Guide
This article will guide you through the process of simplifying the polynomial expression: (5x³ + 2x² + 3)  (3x³ + 8x²  x  1). We will break down the steps involved in reaching the simplified form.
Understanding the Expression
The given expression involves two polynomial expressions:
 (5x³ + 2x² + 3)
 (3x³ + 8x²  x  1)
These expressions are being subtracted from each other.
Simplifying the Expression

Distribute the negative sign: Since we are subtracting the second polynomial, we need to distribute the negative sign to each term inside the parentheses. This changes the expression to:
5x³ + 2x² + 3  3x³  8x² + x + 1

Combine like terms: Now, we group together the terms with the same variable and exponent.
 x³ terms: 5x³  3x³ = 2x³
 x² terms: 2x²  8x² = 6x²
 x terms: + x
 Constant terms: 3 + 1 = 4

Write the simplified expression: After combining the like terms, our simplified expression is:
2x³  6x² + x + 4
Final Thoughts
By following these simple steps, we have successfully simplified the given polynomial expression. The key takeaway is to understand the order of operations and to carefully combine like terms to achieve the simplest form.