%2B(10x%5E4%2B7x%2B5x%5E5).jpeg "(-7x^5+14-2x)+(10x^4+7x+5x^5)")
Simplifying Polynomial Expressions
This article will guide you through the process of simplifying the polynomial expression: (-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5).
Understanding the Basics
Before we begin, let's clarify some key concepts:
- Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents of the variables are non-negative integers.
- Terms: Individual parts of a polynomial separated by addition or subtraction.
- Like Terms: Terms that have the same variable(s) raised to the same power(s).
Simplifying the Expression
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Remove the parentheses: Since we are adding the two polynomials, the parentheses don't affect the order of operations. We can rewrite the expression as:
-7x^5 + 14 - 2x + 10x^4 + 7x + 5x^5
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Identify like terms: Group the terms with the same variables and exponents:
(-7x^5 + 5x^5) + 10x^4 + (-2x + 7x) + 14
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Combine like terms: Perform the indicated operations on the coefficients of the like terms:
-2x^5 + 10x^4 + 5x + 14
Final Result
The simplified form of the polynomial expression (-7x^5 + 14 - 2x) + (10x^4 + 7x + 5x^5) is -2x^5 + 10x^4 + 5x + 14.