(3x^2-x+1)+(15-9x-2x^2)

2 min read Jun 16, 2024
(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.