Simplifying Polynomial Expressions
In mathematics, a polynomial expression is an expression that consists of variables and coefficients, combined using addition, subtraction, and multiplication. To simplify polynomial expressions, we combine like terms. Like terms have the same variables raised to the same powers.
Let's consider the following two polynomial expressions:
 8x^7  6x^5 + 4x^3  6x
 15x^6 + 4x^5  3x^3 + 2
To simplify the expression (8x^7  6x^5 + 4x^3  6x) + (15x^6 + 4x^5  3x^3 + 2), we follow these steps:

Remove the parentheses: Since we are adding the two expressions, we can simply remove the parentheses.
8x^7  6x^5 + 4x^3  6x + 15x^6 + 4x^5  3x^3 + 2

Identify like terms: We group the terms with the same variables and powers.
8x^7 + 15x^6  6x^5 + 4x^5 + 4x^3  3x^3  6x + 2

Combine like terms: We add or subtract the coefficients of the like terms.
8x^7 + 15x^6  2x^5 + x^3  6x + 2
Therefore, the simplified expression is 8x^7 + 15x^6  2x^5 + x^3  6x + 2.
Key points:
 Order of operations: When simplifying expressions, we follow the order of operations (PEMDAS/BODMAS).
 Combining like terms: The coefficients of like terms are added or subtracted. The variable and its exponent remain the same.
 Standard form: It's customary to write polynomials in descending order of powers.
By understanding the process of combining like terms, we can effectively simplify polynomial expressions and make them easier to work with.