(2x+5)(x+1)(3x−5)

Jasonbradley

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Jun 16, 2024

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Expanding and Simplifying the Expression: (2x+5)(x+1)(3x-5)

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

Expanding the Expression

To simplify the expression, we need to expand it. We can do this by multiplying the terms together step by step:

1. Start with the first two factors: (2x+5)(x+1)

   • Apply the distributive property (or FOIL method): (2x+5)(x+1) = 2x(x+1) + 5(x+1)
   • Simplify: 2x² + 2x + 5x + 5 = 2x² + 7x + 5

2. Now multiply the result from step 1 with the third factor: (2x² + 7x + 5)(3x-5)

   • Apply the distributive property again: (2x² + 7x + 5)(3x-5) = 2x²(3x-5) + 7x(3x-5) + 5(3x-5)
   • Simplify: 6x³ - 10x² + 21x² - 35x + 15x - 25

3. Combine like terms: 6x³ + 11x² - 20x - 25

The Simplified Expression

Therefore, the expanded and simplified form of the expression (2x+5)(x+1)(3x-5) is 6x³ + 11x² - 20x - 25.