## Simplifying Algebraic Expressions: A Step-by-Step Guide

This article will walk you through the process of simplifying the algebraic expression: **(6x^2 - 1) + (x^2 + 3) - 2(x^2 - 5) - 15x^2**. We'll break down each step to make it easy to follow.

### Step 1: Distribute

The first step is to distribute any multiplication. In this case, we need to distribute the -2:

(6x^2 - 1) + (x^2 + 3) - 2(x^2 - 5) - 15x^2 = 6x^2 - 1 + x^2 + 3 - 2x^2 + 10 - 15x^2

### Step 2: Combine Like Terms

Now, we need to combine all the terms with the same variable and exponent. Let's group the x^2 terms and the constant terms:

(6x^2 + x^2 - 2x^2 - 15x^2) + (-1 + 3 + 10)

### Step 3: Simplify

Finally, perform the addition and subtraction operations:

-10x^2 + 12

### Conclusion

The simplified form of the algebraic expression **(6x^2 - 1) + (x^2 + 3) - 2(x^2 - 5) - 15x^2** is **-10x^2 + 12**. By following these steps, you can confidently simplify any algebraic expression.