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Which of the following is equivalent to

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Carcass
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Which of the following is equivalent to [#permalink] New post   23 Feb 2021, 02:00
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Which of the following is equivalent to a100−b100a50−b50 for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2



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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: Which of the following is equivalent to [#permalink] New post   23 Feb 2021, 07:32
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Carcass wrote:
Which of the following is equivalent to a100−b100a50−b50 for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2



Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book


The numerator has a nice difference of squares, which can be factored
Note: a^100 = (a^50)²

So, (a^100 - b^100)/(a^50 - b^50) = (a^50 + b^50)(a^50 - b^50)/(a^50 - b^50)
= a^50 + b^50

Answer: C
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Re: Which of the following is equivalent to [#permalink] New post   26 Jan 2022, 07:44
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