## Expanding (x+1)(x-2)(x-7) into Standard Form

This article will guide you through the process of expanding the expression (x+1)(x-2)(x-7) into its standard form, which is a polynomial in descending order of exponents.

### Step 1: Multiply the first two factors

Begin by multiplying the first two factors, (x+1) and (x-2), using the **FOIL** method (First, Outer, Inner, Last):

(x+1)(x-2) = x² - 2x + x - 2 = **x² - x - 2**

### Step 2: Multiply the result by the remaining factor

Now, multiply the result from step 1 (x² - x - 2) by the remaining factor (x-7):

(x² - x - 2)(x - 7) = x²(x - 7) - x(x - 7) - 2(x - 7)

### Step 3: Distribute and simplify

Distribute each term and combine like terms:

x²(x - 7) - x(x - 7) - 2(x - 7) = x³ - 7x² - x² + 7x - 2x + 14
= **x³ - 8x² + 5x + 14**

### Conclusion

Therefore, the standard form of the expression (x+1)(x-2)(x-7) is **x³ - 8x² + 5x + 14**.