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

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

Identify Like Terms: Identify and group the like terms together:
7x^3 + (3x^2 + 6x^2) + 5x + (5  12)

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.