Question

Can someone tell me how to solve this please?
http://desmond.imageshack.us/Himg33/scaled.php?server=33&filename=48085603.jpg&res=medium

Options:
a) 10^12
b) 10^14
c) 10^8
d) 10^10

Answer 1

Do those dots mean multiplication?

Answer 2

Yep, they do

Answer 3

I was just wondering if theres a way to solve that without going through the whole process

Answer 4

im sure there is.. hold on

Answer 5

I'm not used to that form. It's difficult for me to see what's going on there.

Answer 6

Bahrom, can you re-post that in a form I might be able to understand?

Answer 7

(103-3)^4=100^4

Answer 8

How do you know where the parentheses are?

Answer 9

ok let's see:
103^4 - 4 * 103^3 * 3 + 6 * 103^2 * 3^2 - 4 * 103 * 3^3 + 3^4

Answer 10

there are no parethesis, Hero.

Answer 11

parentheses*

Answer 12

http://en.wikipedia.org/wiki/Binomial_theorem

Answer 13

103^4 - 103^3 * 2^2 * 3 + 103^2 * 2 * 3^3 - 2^2 * 103 * 3^3 + 3^4

Answer 14

hold on let me write this out on paper.. i got lost in powers lol

Answer 15

Interesting cinar. I'm used to x's and y's being there to use binomial theorem.

Answer 16

that is (x+y)^4, where x = 100, y = 3

Answer 17

we can show that by grouping.. (i think) trying to get into the form (100+3)^2 (100+3)^2 gimme a sec.

Answer 18

mehh.. grouped wrong.. these 103s are annoying.. hold on, this is one of those problems that's going to nag me until i get it right haha will get there eventually..

Answer 19

This is the binomial expansion of \((103 - 3)^4 = 100^4 = 100,000,000\) The way I saw this quickly is by noticing that the first coefficient of each term is 1, 4, 6, 4, 1 from first to last. Those correspond to 4-choose-0, 4-choose-1, 4-choose-2, 4-choose-3, and 4-choose-4 respectively.

Also, the very first term was \(103^4\) which means that 103 is the first term in the binomial you want to expand. Likewise, \(3^4\) was the last, so 3 was the other term.

Finally, I knew that it was \((103-3)^4\) instead of \((103+3)^4\) because there were alternating plus and minus signs.

Does this make sense?

Answer 20

If you want it as one of the options, notice that \(100^4 = (10^2)^4=10^8\)

Answer 21

Oh, thank you so much! I appreciate your answers.

Answer 22

You're very welcome.