(x+1)(x+8)(2x+3)

2 min read Jun 16, 2024

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.