(-8y^2-9y)-(-8y^3+9y^2-5y)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (-8y^2-9y)-(-8y^3+9y^2-5y)

This article will guide you through the process of simplifying the algebraic expression (-8y^2-9y)-(-8y^3+9y^2-5y).

Understanding the Expression

The expression consists of two sets of terms enclosed in parentheses, with a subtraction sign separating them. To simplify it, we need to perform the following steps:

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1.

2. Combine like terms: After distributing the negative sign, we'll identify terms with the same variables and exponents and combine their coefficients.

Step-by-Step Simplification

Let's break down the simplification:

1. Distribute the negative sign:

   (-8y^2 - 9y) + (8y^3 - 9y^2 + 5y)

2. Combine like terms:

   • y^3 terms: 8y^3
   • y^2 terms: -8y^2 - 9y^2 = -17y^2
   • y terms: -9y + 5y = -4y

3. Write the simplified expression:

   8y^3 - 17y^2 - 4y

Conclusion

By following the steps of distributing the negative sign and combining like terms, we successfully simplified the expression (-8y^2-9y)-(-8y^3+9y^2-5y) to 8y^3 - 17y^2 - 4y. This process demonstrates the fundamental principles of simplifying algebraic expressions.