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Cuz i had this question

Here is hunch:

An expression like x * y keeps the number of zeroes as long as x and y do not contain (2 * 5) or any factor of ten like (25 * 4) etc.

Ex: one zero (10 * 11 = 110) four zeroes (100 * 100 = 10,000)

 - In the current problem, the numbers obviously do not have any factor of ten. So:

1,000,000,000,002 * 999,999,999,996​ we count the zeroes, getting an answer of \(\boxed{11}\)?

I saw you asking for hw questions. It is all in your history. Stop being such a hypocrite. Also, aren't we supposed to ask for help when we have a question with hw? This place is for questions, and why don't you stop criticising and actually try to help, like Cal is doing!

Thats how i did it at least.

This is aops hw so we cant help you with it! I can give you a hint though! Find out how long it takes 1 person to paint the wall.

It lit says above.... Oh sorry the end is an 9 not an 8

I never said that!

But you said... wait now I'm super confused and I lost my train of thought

i was in prealgebra last year as well and this is the course i took afterwards, 'you know'.

But you said that it ended with a 9 a few minutes ago.....

4x - 3y  =  2a   --->   multiply by 3   --->   12x - 9y  =  6a

2x + y  =  3a   --->   multiply by -2   --->   -4x - 2y  =  -6a

Add down the columns:                            8x - 11y  =  0   --->   11y  =  8x   --->   y  =  (8/11)·x

Since x = 3:   y  =  (8/11)·x   --->   y  =  (8/11)·3   --->   y  =  24/11

x = 3  and  y = 24/11   --->   4x - 3y  =  2a   --->   4(3) - 3(24/11)  =  60/11  =  2a   --->   a  =  30/11

Please read the question

I am just wondering how to do this without a calculator.

1,000,000,000,002 * 999,999,999,996

How will we know how many zeros that has?

Wait a sec didnt you say its 999,999,999? If it is that then it should be (100,000,000-1)^2 right?

maybe something like 1000000000000^2-1000000000000*2*2+4?

ohh i didn't think of it that way. thanks !

Good idea!

_________

So by the (a - b)² = (a + b)(a - b), can we work this further? I am struggling as much as you right now.

wrong. 

maybe (1000000000000-2)^2?