## Simplifying the Expression: (x^2-4)(x+3)-(x^2+2x-5)

This article will guide you through the process of simplifying the algebraic expression: **(x^2-4)(x+3)-(x^2+2x-5)**. We will break down the steps involved in order to arrive at a simplified form.

### Step 1: Expanding the First Product

The first part of the expression involves multiplying two binomials: **(x^2-4)(x+3)**. We can use the distributive property (or FOIL method) to expand this product:

**x^2 * x = x^3****x^2 * 3 = 3x^2****-4 * x = -4x****-4 * 3 = -12**

Combining these terms, we get: **x^3 + 3x^2 - 4x - 12**

### Step 2: Simplifying the Entire Expression

Now we can rewrite the entire expression with the expanded product:

**(x^3 + 3x^2 - 4x - 12) - (x^2 + 2x - 5)**

Next, we distribute the negative sign in front of the second set of parentheses:

**x^3 + 3x^2 - 4x - 12 - x^2 - 2x + 5**

### Step 3: Combining Like Terms

Finally, we combine the like terms to obtain the simplified expression:

**x^3 + (3x^2 - x^2) + (-4x - 2x) + (-12 + 5)**

This results in: **x^3 + 2x^2 - 6x - 7**

### Conclusion

Therefore, the simplified form of the expression **(x^2-4)(x+3)-(x^2+2x-5)** is **x^3 + 2x^2 - 6x - 7**. This process demonstrates how to systematically simplify algebraic expressions through expansion and combining like terms.