%2B(6x%5E3-x%5E2-5x).jpeg "(2x^3+3x^2+4)+(6x^3-x^2-5x)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through simplifying the polynomial expression (2x³ + 3x² + 4) + (6x³ - x² - 5x). We'll break down the process into easy-to-follow steps.
Understanding Polynomials
Before we dive in, let's quickly review what polynomials are:
- Polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms are individual parts of a polynomial separated by addition or subtraction.
- Coefficients are the numerical values multiplying the variables.
- Variables are the letters representing unknown values.
Simplifying the Expression
Step 1: Identify Like Terms
Like terms are terms that have the same variables raised to the same powers. In our expression, we have:
- x³ terms: 2x³ and 6x³
- x² terms: 3x² and -x²
- x terms: -5x
- Constant terms: 4 and -5
Step 2: Combine Like Terms
Now, we simply add the coefficients of like terms:
- x³ terms: 2x³ + 6x³ = 8x³
- x² terms: 3x² - x² = 2x²
- x terms: -5x
- Constant terms: 4 - 5 = -1
Step 3: Write the Simplified Expression
Finally, we combine all the simplified terms:
8x³ + 2x² - 5x - 1
Conclusion
We have successfully simplified the polynomial expression (2x³ + 3x² + 4) + (6x³ - x² - 5x) into 8x³ + 2x² - 5x - 1. Remember, the key to simplifying polynomials is to identify like terms and combine them by adding or subtracting their coefficients.