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Determine the product (x^1/3 + y^1/3)(x^2/3 - x^1/3 y^1/3 + y^2/3) without using long...

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spock10 | Student, Undergraduate | Honors

Posted May 2, 2012 at 2:35 PM via web

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Determine the product (x^1/3 + y^1/3)(x^2/3 - x^1/3 y^1/3 + y^2/3) without using long multiplication. 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 2, 2012 at 2:53 PM (Answer #1)

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The product `(x^(1/3) + y^(1/3))(x^(2/3) - x^(1/3)*y^(1/3) + y^(2/3))` has to be determined without using conventional multiplication.

If `x^(1/3)` = a and `y^(1/3)` = b, the given expression is:

(a + b)(a^2 - ab + b^2)

=> a^3 + b^3

=> x + y

The product `(x^(1/3) + y^(1/3))(x^(2/3) - x^(1/3)*y^(1/3) + y^(2/3)) = x + y`

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