(-5u^3v^4+9u)+(-5u^3v^4-8u+8u^2v^2)+(-8u^4v^2+8u^3v^4)

2 min read Jun 16, 2024

Simplifying Polynomial Expressions

This article will guide you through simplifying the polynomial expression:

(-5u^3v^4+9u)+(-5u^3v^4-8u+8u^2v^2)+(-8u^4v^2+8u^3v^4)

Before we dive into simplification, let's understand the key components of this expression:

Polynomial: An expression with multiple terms, each consisting of a variable raised to a non-negative integer power, multiplied by a coefficient.
Terms: The individual parts of a polynomial separated by addition or subtraction.
Coefficient: The numerical factor that multiplies a variable.
Variable: A symbol that represents an unknown quantity.
Exponent: The power to which a variable is raised.

Remove Parentheses: Since all the parentheses are preceded by a plus sign, we can simply remove them:

-5u^3v^4 + 9u - 5u^3v^4 - 8u + 8u^2v^2 - 8u^4v^2 + 8u^3v^4
Combine Like Terms: Look for terms with the same variable and exponent combination.
- u^3v^4 terms: -5u^3v^4 - 5u^3v^4 + 8u^3v^4 = -2u^3v^4
- u terms: 9u - 8u = u
- u^2v^2 term: 8u^2v^2 (remains unchanged)
- u^4v^2 term: -8u^4v^2 (remains unchanged)
Rewrite the Simplified Expression: Combine the simplified terms:

-8u^4v^2 - 2u^3v^4 + 8u^2v^2 + u

The simplified form of the given polynomial expression is: -8u^4v^2 - 2u^3v^4 + 8u^2v^2 + u