(-x4+13x5+6x3)+(6x3+5x5+7x4)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

(-x⁴ + 13x⁵ + 6x³) + (6x³ + 5x⁵ + 7x⁴)

Understanding Polynomials

A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents of the variables are non-negative integers.

Steps to Simplify

1. Identify Like Terms: Like terms have the same variable and the same exponent. In our expression, we have the following pairs of like terms:

   • -x⁴ and 7x⁴
   • 13x⁵ and 5x⁵
   • 6x³ and 6x³

2. Combine Like Terms: Combine the coefficients of the like terms while keeping the variable and exponent the same.

   • (-x⁴ + 7x⁴) = 6x⁴
   • (13x⁵ + 5x⁵) = 18x⁵
   • (6x³ + 6x³) = 12x³

3. Write the Simplified Expression: Combine the simplified terms in descending order of their exponents:

   18x⁵ + 6x⁴ + 12x³

Conclusion

Therefore, the simplified form of the polynomial expression (-x⁴ + 13x⁵ + 6x³) + (6x³ + 5x⁵ + 7x⁴) is 18x⁵ + 6x⁴ + 12x³.