(x^1/6+2)(x^1/3-2x^1/6+4)

Jasonbradley

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Jun 17, 2024

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Expanding the Expression: (x^(1/6) + 2)(x^(1/3) - 2x^(1/6) + 4)

This expression involves fractional exponents, which can seem intimidating at first. However, we can expand it using the distributive property (also known as FOIL for binomials) and simplify the result.

Steps to Expand:

1. Distribute the first term of the first binomial:

   • x^(1/6) * (x^(1/3) - 2x^(1/6) + 4) = x^(1/6 + 1/3) - 2x^(1/6 + 1/6) + 4x^(1/6)

2. Distribute the second term of the first binomial:

   • 2 * (x^(1/3) - 2x^(1/6) + 4) = 2x^(1/3) - 4x^(1/6) + 8

3. Combine the results from steps 1 and 2:

   • x^(1/6 + 1/3) - 2x^(1/6 + 1/6) + 4x^(1/6) + 2x^(1/3) - 4x^(1/6) + 8

4. Simplify the exponents:

   • x^(1/2) - 2x^(1/3) + 4x^(1/6) + 2x^(1/3) - 4x^(1/6) + 8

5. Combine like terms:

   • x^(1/2) + 8

Final Expanded Form:

Therefore, the expanded form of (x^(1/6) + 2)(x^(1/3) - 2x^(1/6) + 4) is x^(1/2) + 8.