%2B(12%2Bx-6x%5E4)-(x%5E4-x%5E2).jpeg "(10x+8x^5-2)+(12+x-6x^4)-(x^4-x^2)")
Simplifying Polynomial Expressions
This article will guide you through simplifying the polynomial expression: (10x+8x^5-2)+(12+x-6x^4)-(x^4-x^2). We will break down the process step by step, making it easy to understand.
Step 1: Removing Parentheses
First, we need to remove the parentheses from the expression. Remember that a plus sign in front of a parenthesis doesn't change the signs inside, while a minus sign changes all the signs inside.
Applying this rule, we get:
10x + 8x^5 - 2 + 12 + x - 6x^4 - x^4 + x^2
Step 2: Combining Like Terms
Next, we combine the terms that have the same variable and exponent. For example, '10x' and 'x' can be combined, and '-6x^4' and '-x^4' can be combined.
Let's rearrange the terms:
8x^5 - 6x^4 - x^4 + x^2 + 10x + x - 2 + 12
Combining like terms:
8x^5 - 7x^4 + x^2 + 11x + 10
Step 3: Final Simplified Expression
The final simplified expression is: 8x^5 - 7x^4 + x^2 + 11x + 10.
Conclusion
By carefully following these steps, we have successfully simplified the polynomial expression. This process involves removing parentheses, combining like terms, and arranging the terms in descending order of their exponents. Understanding how to simplify polynomial expressions is a fundamental skill in algebra, allowing us to analyze and solve various equations and problems.