## Expanding the Expression: (x^3 + 3x^2 - 2x + 5)(x - 7)

This article will guide you through the process of expanding the given expression: **(x^3 + 3x^2 - 2x + 5)(x - 7)**. This involves multiplying each term within the first set of parentheses by each term in the second set of parentheses.

### Applying the Distributive Property

We will apply the distributive property twice to expand this expression. This means we'll multiply each term in the first set of parentheses by **x** and then by **-7**.

Let's break down the steps:

**Step 1:** Multiply each term in the first set of parentheses by **x**:

- x^3 * x =
**x^4** - 3x^2 * x =
**3x^3** - -2x * x =
**-2x^2** - 5 * x =
**5x**

**Step 2:** Multiply each term in the first set of parentheses by **-7**:

- x^3 * -7 =
**-7x^3** - 3x^2 * -7 =
**-21x^2** - -2x * -7 =
**14x** - 5 * -7 =
**-35**

### Combining Like Terms

Now, we combine the terms we obtained in the previous steps, remembering to pay attention to the signs:

**x^4**- 3x^3 - 7x^3 =
**-4x^3** - -2x^2 - 21x^2 =
**-23x^2** - 5x + 14x =
**19x** **-35**

### Final Expanded Expression

Therefore, the expanded form of the expression (x^3 + 3x^2 - 2x + 5)(x - 7) is:

**x^4 - 4x^3 - 23x^2 + 19x - 35**