## Simplifying the Expression: (x-3)(x+7) - (x+5)(x-1)

This article will guide you through simplifying the expression **(x-3)(x+7) - (x+5)(x-1)**. We'll use the distributive property and basic algebraic operations to arrive at a simplified form.

### Expanding the Expressions

First, let's expand the products using the distributive property:

**(x-3)(x+7) = x(x+7) - 3(x+7)****(x+5)(x-1) = x(x-1) + 5(x-1)**

Now, let's distribute further:

**x(x+7) - 3(x+7) = x² + 7x - 3x - 21****x(x-1) + 5(x-1) = x² - x + 5x - 5**

### Combining Like Terms

Let's combine like terms in both expressions:

**x² + 7x - 3x - 21 = x² + 4x - 21****x² - x + 5x - 5 = x² + 4x - 5**

### Subtracting the Expressions

Now, we can substitute these simplified expressions back into the original equation:

**(x-3)(x+7) - (x+5)(x-1) = (x² + 4x - 21) - (x² + 4x - 5)**

Subtracting the second expression from the first, we get:

**(x² + 4x - 21) - (x² + 4x - 5) = x² + 4x - 21 - x² - 4x + 5**

### Final Simplification

Finally, we can combine the like terms again:

**x² + 4x - 21 - x² - 4x + 5 = -16**

Therefore, the simplified expression for **(x-3)(x+7) - (x+5)(x-1)** is **-16**.