exponents

[beater]

99,9992^2 - 1^2 =

A. 10^10 - 2
B. (10^5 – 2)^2
C. 10^4(10^5 – 2)
D. 10^5(10^4 – 2)
E. 10^5(10^5 – 2)

I made a silly error and messed up this one. I'd like to see your approach. pLease show your workings. Thanks

[nikhilagrawal]

E is the answer

[csandeepreddy]

99,999^2 - 1^2 can be written as

(100,000 - 1)^2 - 1^2
=>(10^5 - 1)^2 - 1^2
=>10^10 + 1 - 2*10^5 - 1 -----------using (a - b)^2 = a^2 + b^2 - 2ab
=>10^10 - 2*10^5
=>10^5(10^5 - 2)

IMO E

[cramya]

There is a typo in the original problem.

Its mentioned as 99,9992^2 - 1^2 = but it really is

99,999^2 - 1^2 =

[lunarpower]

99,999^2 - 1^2 can be written as

(100,000 - 1)^2 - 1^2
=>(10^5 - 1)^2 - 1^2
=>10^10 + 1 - 2*10^5 - 1 -----------using (a - b)^2 = a^2 + b^2 - 2ab
=>10^10 - 2*10^5
=>10^5(10^5 - 2)

IMO E

you could do that, and you would be fine.

BUT

you should notice that THIS IS ALREADY A DIFFERENCE OF SQUARES.
it's just so ... perfect. it's like a nice juicy steak on a silver platter, at the perfect temperature for human consumption; the solution above, while 100% correct, is somewhat akin to putting that perfect steak back into the microwave for 30 more seconds.

here's how to take a nice big juicy bite:
99,999^2 - 1^2
= (99,999 - 1)(99,999 + 1)
= (99,998)(100,000)
= (10^5 - 2)(10^5)
done

notice that you have to pick up on the fact that 10^5 is the same thing as 100,000.
but you should know that.
put it on a flash card if you don't.

while you're at it, also make a flash card for the difference of squares.
and if you didn't recognize the difference of squares within 3 seconds, then drop and give me 100 pushups. right now.

flash cards are your friends.

[sumidi]

Ron your solution made me smile ....thats brilliant!

[niraj_a]

ron, that was just brilliant!!!!

should notice a^2 - b^2 more often.

[rabab]

Lol. Way to go Ron! Loved your reply.