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explain solution for an algebraic expression

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explain solution for an algebraic expression

by stormgal » Mon Jun 14, 2010 6:19 pm
The following problem is from the Nova book:

1111.5^2 - 999.5^2 =


The solution is
=(1111.5-999.5)(1111.5+999.5)
=(1111+0.5 - 999-0.5)(1111+0.5+999+0.5)
=(1111-999)(1111+999+1)
=(1111-999)(1111+999)+(1111-999)

=1111^2-9999^2+(1111-999)

(then it solves from there to -121) But can somebody please explain what I've highlighted in red - I don't understand where that expression came from.
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by Rahul@gurome » Mon Jun 14, 2010 6:57 pm
Let (1111 - 999) be "a" and let (1111 + 999) be "b".
So (1111 - 999)(1111 + 999 +1) = a*(b+1) = a*b+a on expansion
which is (1111 - 999)*(1111 + 999) + (1111 - 999) = 1111^2 - 999^2 + 1111 - 999.

I hope the steps are clear now.
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by selango » Mon Jun 14, 2010 9:58 pm
These types of long algebraic expressions wont appear in real GMAT
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by hardik.jadeja » Tue Jun 15, 2010 10:55 am
selango wrote:These types of long algebraic expressions wont appear in real GMAT
Actually, its not that long.. It's definitely manageable.

1111.5^2 - 999.5^2 =
= (1111.5-999.5)(1111.5+999.5)
= (112)(2111)
= 236432
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by amising6 » Tue Jun 15, 2010 9:43 pm
1111.5^2 - 999.5^2 =

1111.5 =a
999.5=b
we know a^2-b^2=(a-b)*(a+b)
1111.5^2 - 999.5^2=(1111.5+999.5)(1111.5-999.5)
=2111*112
=2111(100+12)
=211100+25332=
236432
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