## Simplifying the Expression: (7x³ - 1) - (15x³ + 4x² - x + 3)

In this article, we will explore the simplification of the expression **(7x³ - 1) - (15x³ + 4x² - x + 3)**. This process involves understanding the basic principles of polynomial subtraction and applying them to combine like terms.

### Step 1: Distribute the Negative Sign

The first step is to distribute the negative sign in front of the second set of parentheses. This means multiplying each term inside the second parentheses by -1.

**(7x³ - 1) + (-1)(15x³ + 4x² - x + 3)**

This gives us:

**(7x³ - 1) - 15x³ - 4x² + x - 3**

### Step 2: Combine Like Terms

Now, we can combine the terms that have the same variable and exponent.

**x³ terms:**7x³ - 15x³ = -8x³**x² terms:**-4x²**x terms:**+x**Constant terms:**-1 - 3 = -4

### Step 3: Final Expression

Combining all the simplified terms, we arrive at the simplified expression:

**-8x³ - 4x² + x - 4**

Therefore, the simplified form of the expression **(7x³ - 1) - (15x³ + 4x² - x + 3)** is **-8x³ - 4x² + x - 4**.

### Conclusion

By applying the basic principles of polynomial subtraction, we have successfully simplified the given expression. This process involved distributing the negative sign, identifying and combining like terms, and presenting the final simplified form. This example demonstrates the importance of understanding the properties of polynomials for performing algebraic operations.