## 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.