%2B(2u%5E3-7u%2B6).jpeg "(2u^3+6u^2+3)+(2u^3-7u+6)")
Simplifying Polynomial Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the expression (2u^3 + 6u^2 + 3) + (2u^3 - 7u + 6). We will break down the steps involved and explain the underlying concepts.
Understanding the Expression
The expression consists of two sets of terms enclosed in parentheses. These sets represent polynomials, which are expressions involving variables raised to non-negative integer powers.
Simplifying Using the Distributive Property
The first step is to remove the parentheses. Since we are adding the two polynomials, we can simply distribute the positive sign. This means we can remove the parentheses without changing any of the signs within them:
2u^3 + 6u^2 + 3 + 2u^3 - 7u + 6
Combining Like Terms
Now, we need to combine like terms. Like terms have the same variable and exponent. For example, 2u^3 and 2u^3 are like terms, while 6u^2 and -7u are not.
- Combine the u^3 terms: 2u^3 + 2u^3 = 4u^3
- Combine the u^2 terms: 6u^2
- Combine the u terms: -7u
- Combine the constant terms: 3 + 6 = 9
The Simplified Expression
After combining like terms, we get the simplified expression:
4u^3 + 6u^2 - 7u + 9
Key Concepts
- Polynomial: An expression involving variables raised to non-negative integer powers.
- Like Terms: Terms with the same variable and exponent.
- Distributive Property: Allows us to remove parentheses by multiplying each term inside the parentheses by the factor outside.
By following these steps, you can effectively simplify polynomial expressions and understand the fundamental principles involved.