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GMATT73
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 04:44
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) to one binomial expression.



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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 05:22
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When did GMAT start testing binomial theorem ?
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GMATT73
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 07:25
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jainan24
When did GMAT start testing binomial theorem ?
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Not sure, but iI believe the BT is listed in the OG10 (2000~).

BG got it. :-D
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Rayn
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 09:08
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GMATT73
Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) to one binomial expression.
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Could someone please do a step by step process with this please...
I do not quite understand what the dots mean here (...)

:?: :?: :?:
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Amit05
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 09:40
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I too got x^128 - y^128.

My approach was : (x^2 - y^2)(x^2 + y^2) = (x^4 - y^4)
(x^4 - y^4) (x^4 + y^4) = (x^8 - y^8)
(x^8 - y^8) (x^8 + y^8) = (x^16 - y^16)
...
...
..
...
= (x^128 - y^128)

But I think this is lengthy.

Can anyone please suggest if this is the right approach and also if there is any better one.

Regards,
Amit
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Rayn
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Simplify (x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)...(x^64+y^64)(x-y) 07 Oct 2006, 12:05
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Okay, makes sense...you're right. Thats the trick.

Difference of two squares. 8-)



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