## Expanding and Simplifying (x+1)(x+8)(2x+3)

This article will explore the process of expanding and simplifying the algebraic expression **(x+1)(x+8)(2x+3)**. This involves applying the distributive property multiple times to remove the parentheses and then combining like terms.

### Step 1: Expanding the first two factors

We start by expanding the first two factors, **(x+1)(x+8)**, using the distributive property (also known as FOIL):

**(x+1)(x+8) = x(x+8) + 1(x+8)****= x² + 8x + x + 8****= x² + 9x + 8**

### Step 2: Expanding the result with the third factor

Now, we multiply the result from Step 1, **x² + 9x + 8**, with the third factor, **(2x+3):**

**(x² + 9x + 8)(2x+3) = x²(2x+3) + 9x(2x+3) + 8(2x+3)**

### Step 3: Applying the distributive property again

We distribute each term in the first set of parentheses to the terms in the second set:

**= 2x³ + 3x² + 18x² + 27x + 16x + 24**

### Step 4: Combining like terms

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

**= 2x³ + 21x² + 43x + 24**

### Conclusion

Therefore, the expanded and simplified form of **(x+1)(x+8)(2x+3)** is **2x³ + 21x² + 43x + 24**. This process demonstrates how to handle multiplications of multiple binomials using the distributive property and combining like terms.