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

2 min read Jun 17, 2024
(x+8)(x-3)(2x+1)

Expanding and Simplifying the Expression (x+8)(x-3)(2x+1)

This article will guide you through expanding and simplifying the expression (x+8)(x-3)(2x+1).

Step 1: Multiply the first two factors

Begin by multiplying the first two factors, (x+8) and (x-3):

  • (x+8)(x-3) = x² - 3x + 8x - 24
  • = x² + 5x - 24

Step 2: Multiply the result by the third factor

Now, multiply the simplified result from Step 1 (x² + 5x - 24) by the third factor (2x + 1):

  • (x² + 5x - 24)(2x + 1)
  • = 2x³ + x² + 10x² + 5x - 48x - 24

Step 3: Combine like terms

Finally, combine the like terms to get the simplified expression:

  • = 2x³ + 11x² - 43x - 24

Therefore, the expanded and simplified form of (x+8)(x-3)(2x+1) is 2x³ + 11x² - 43x - 24.

Key takeaways

  • FOIL method: You can use the FOIL (First, Outer, Inner, Last) method to multiply binomials.
  • Distributive Property: The distributive property is used to multiply polynomials.
  • Combine like terms: Combining like terms simplifies the expression and makes it easier to work with.

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