%2B(15-9x-2x%5E2).jpeg "(3x^2-x+1)+(15-9x-2x^2)")
Simplifying Polynomial Expressions
This article will demonstrate how to simplify the polynomial expression: (3x^2 - x + 1) + (15 - 9x - 2x^2)
Understanding the Process
To simplify this expression, we need to combine like terms. Like terms are terms that have the same variable and exponent.
Step 1: Remove the Parentheses
Since we are adding the two polynomials, the parentheses don't affect the signs of the terms. We can simply remove them:
3x^2 - x + 1 + 15 - 9x - 2x^2
Step 2: Combine Like Terms
Identify and group the like terms together:
- x^2 terms: 3x^2 - 2x^2
- x terms: -x - 9x
- Constant terms: 1 + 15
Step 3: Simplify
Now, combine the coefficients of the like terms:
- x^2 terms: (3 - 2)x^2 = x^2
- x terms: (-1 - 9)x = -10x
- Constant terms: 1 + 15 = 16
Step 4: Final Expression
Combine all the simplified terms to get the final expression:
x^2 - 10x + 16
Conclusion
Therefore, the simplified form of the polynomial expression (3x^2 - x + 1) + (15 - 9x - 2x^2) is x^2 - 10x + 16.