(6a^2-5a)+(a-5a+3a^3)

2 min read Jun 16, 2024

Simplifying the Expression: (6a^2 - 5a) + (a - 5a + 3a^3)

This article will guide you through simplifying the algebraic expression: (6a^2 - 5a) + (a - 5a + 3a^3).

Step 1: Identify Like Terms

First, we need to identify the like terms within the expression. Like terms are terms that have the same variable and the same exponent.

6a^2 and 3a^3 are not like terms because they have different exponents.
-5a, a, and -5a are like terms because they all have the variable "a" raised to the power of 1.

Step 2: Combine Like Terms

Now, we can combine the like terms by adding their coefficients:

6a^2 + 3a^3 remains as it is (no other terms have the same exponent).
-5a + a - 5a = -9a

Step 3: Write the Simplified Expression

After combining like terms, the simplified expression is:

3a^3 + 6a^2 - 9a

Conclusion

By identifying like terms and combining them, we successfully simplified the expression (6a^2 - 5a) + (a - 5a + 3a^3) to 3a^3 + 6a^2 - 9a. Remember, this process is crucial for solving algebraic equations and simplifying complex expressions in mathematics.