%2B(-7x%5E3%2B12x%5E5%2B6x%5E2).jpeg "(4+3x^2+8x^3)+(-7x^3+12x^5+6x^2)")
Simplifying Polynomials: A Step-by-Step Guide
This article will guide you through the process of simplifying the polynomial expression:
(4 + 3x² + 8x³) + (-7x³ + 12x⁵ + 6x²)
Understanding Polynomials
Before diving into the simplification, let's define what a polynomial is. A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
Simplifying the Expression
To simplify the given expression, we follow these steps:
-
Remove the parentheses: Since we are adding the two polynomials, the parentheses simply indicate grouping and don't affect the operations. We can rewrite the expression as:
4 + 3x² + 8x³ - 7x³ + 12x⁵ + 6x²
-
Combine like terms: Like terms have the same variable and exponent. We combine the coefficients of the like terms:
- x⁵ terms: 12x⁵
- x³ terms: 8x³ - 7x³ = x³
- x² terms: 3x² + 6x² = 9x²
- Constant term: 4
-
Write the simplified expression: Combining all the terms, we get the simplified polynomial:
12x⁵ + x³ + 9x² + 4
Conclusion
Therefore, the simplified form of the polynomial expression (4 + 3x² + 8x³) + (-7x³ + 12x⁵ + 6x²) is 12x⁵ + x³ + 9x² + 4. By following these steps, you can simplify any polynomial expression with ease.