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(2y^2-5y+1)+(y^2-y-4)

2 min read Jun 16, 2024
(2y^2-5y+1)+(y^2-y-4)

Simplifying Polynomial Expressions: (2y^2-5y+1)+(y^2-y-4)

This article will guide you through the process of simplifying the polynomial expression (2y^2-5y+1)+(y^2-y-4).

Understanding the Basics

Before we dive into the simplification, let's understand some key terms:

  • Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, with non-negative integer exponents.
  • Terms: The individual parts of a polynomial separated by addition or subtraction. For example, in 2y^2-5y+1, the terms are 2y^2, -5y, and 1.
  • Like Terms: Terms that have the same variable and exponent. For example, 2y^2 and y^2 are like terms, but 2y^2 and -5y are not.

Simplifying the Expression

  1. Identify Like Terms: In the expression (2y^2-5y+1)+(y^2-y-4), identify the like terms:

    • y^2 terms: 2y^2 and y^2
    • y terms: -5y and -y
    • Constant terms: 1 and -4

  2. Combine Like Terms: Add the coefficients of each set of like terms:

    • y^2 terms: 2y^2 + y^2 = 3y^2
    • y terms: -5y - y = -6y
    • Constant terms: 1 - 4 = -3

  3. Write the Simplified Expression: Combine the results from step 2:

    • 3y^2 - 6y - 3

Conclusion

The simplified form of the polynomial expression (2y^2-5y+1)+(y^2-y-4) is 3y^2 - 6y - 3. Remember, to simplify polynomials, we combine like terms by adding their coefficients.

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