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

Jasonbradley

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Jun 16, 2024

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

This article will guide you through expanding the expression (2x-5)(4x^2-3x+1). This involves applying the distributive property (also known as FOIL method) to multiply each term in the first expression by each term in the second expression.

Expanding the Expression

1. Distribute the first term of the first expression:

   • 2x multiplied by 4x^2 gives 8x^3
   • 2x multiplied by -3x gives -6x^2
   • 2x multiplied by 1 gives 2x

2. Distribute the second term of the first expression:

   • -5 multiplied by 4x^2 gives -20x^2
   • -5 multiplied by -3x gives 15x
   • -5 multiplied by 1 gives -5

3. Combine all the terms:

   • 8x^3 - 6x^2 + 2x - 20x^2 + 15x - 5

4. Simplify by combining like terms:

   • 8x^3 - 26x^2 + 17x - 5

Final Result

Therefore, the expanded form of (2x-5)(4x^2-3x+1) is 8x^3 - 26x^2 + 17x - 5.