(-2y^5+y^3-2y)-(y^5-4y^3+6)=

2 min read Jun 16, 2024

Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the polynomial expression:

(-2y^5 + y^3 - 2y) - (y^5 - 4y^3 + 6)

Before we begin, let's recall some fundamental concepts:

Polynomials: Expressions consisting of variables and coefficients combined using addition, subtraction, and multiplication.
Terms: Individual parts of a polynomial separated by addition or subtraction.
Like Terms: Terms with the same variable and exponent.
Combining Like Terms: Adding or subtracting coefficients of like terms.

Distribute the Negative Sign:
- The minus sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1.
- This gives us:
  -2y^5 + y^3 - 2y - y^5 + 4y^3 - 6
Identify Like Terms:
- y^5 terms: -2y^5 - y^5
- y^3 terms: y^3 + 4y^3
- y terms: -2y
- Constant term: -6
Combine Like Terms:
- y^5 terms: -2y^5 - y^5 = -3y^5
- y^3 terms: y^3 + 4y^3 = 5y^3
- y terms: -2y
- Constant term: -6
Write the Simplified Expression:
- Combining all the simplified terms, we get: -3y^5 + 5y^3 - 2y - 6

Therefore, the simplified form of the polynomial expression (-2y^5 + y^3 - 2y) - (y^5 - 4y^3 + 6) is -3y^5 + 5y^3 - 2y - 6.