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(3x-4)(5-2x)(4x+1)

2 min read Jun 16, 2024
(3x-4)(5-2x)(4x+1)

Expanding the Expression (3x-4)(5-2x)(4x+1)

This article will guide you through the process of expanding the given expression: (3x-4)(5-2x)(4x+1).

Understanding the Process

Expanding an expression like this involves using the distributive property multiple times. Here's the breakdown:

  1. Multiply the first two factors: We will start by expanding (3x-4)(5-2x).
  2. Multiply the result by the third factor: We will then multiply the result from step 1 by (4x+1).

Expanding the First Two Factors

Let's expand (3x-4)(5-2x):

  • Distribute 3x over (5-2x):
    • 3x * 5 = 15x
    • 3x * -2x = -6x²
  • Distribute -4 over (5-2x):
    • -4 * 5 = -20
    • -4 * -2x = 8x
  • Combine the terms:
    • 15x - 6x² - 20 + 8x = -6x² + 23x - 20

Expanding the Entire Expression

Now we have: (-6x² + 23x - 20)(4x+1)

Let's repeat the distributive property:

  • Distribute -6x² over (4x+1):
    • -6x² * 4x = -24x³
    • -6x² * 1 = -6x²
  • Distribute 23x over (4x+1):
    • 23x * 4x = 92x²
    • 23x * 1 = 23x
  • Distribute -20 over (4x+1):
    • -20 * 4x = -80x
    • -20 * 1 = -20
  • Combine the terms:
    • -24x³ - 6x² + 92x² + 23x - 80x - 20 = -24x³ + 86x² - 57x - 20

Final Result

Therefore, the expanded form of the expression (3x-4)(5-2x)(4x+1) is -24x³ + 86x² - 57x - 20.

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