%2B(-12%2B5x%2B6x%5E2).jpeg "(5+7x^3+3x^2)+(-12+5x+6x^2)")
Simplifying Polynomial Expressions: (5+7x^3+3x^2)+(-12+5x+6x^2)
This article will guide you through simplifying the polynomial expression (5+7x^3+3x^2)+(-12+5x+6x^2).
Understanding the Basics
Before diving into the simplification process, let's clarify some key concepts:
- Polynomial: A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Terms: In a polynomial, each individual expression separated by addition or subtraction is called a term. For example, in 5 + 7x^3 + 3x^2, we have three terms: 5, 7x^3, and 3x^2.
- Like Terms: Like terms have the same variable raised to the same power. For example, 3x^2 and 6x^2 are like terms, but 3x^2 and 5x are not.
Simplifying the Expression
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Remove the parentheses: Since we are adding the two expressions, the parentheses don't affect the order of operations. We can simply remove them:
(5+7x^3+3x^2) + (-12+5x+6x^2) = 5 + 7x^3 + 3x^2 - 12 + 5x + 6x^2
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Identify Like Terms: Identify and group the like terms together:
7x^3 + (3x^2 + 6x^2) + 5x + (5 - 12)
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Combine Like Terms: Combine the coefficients of the like terms:
7x^3 + 9x^2 + 5x - 7
Final Result
The simplified form of the polynomial expression (5+7x^3+3x^2)+(-12+5x+6x^2) is 7x^3 + 9x^2 + 5x - 7.