Question

Determine the most efficient way to use the Binomial Theorem to show the following.
(11)^4=14641
a.write 11-5+6 and expand.
b.write 11=10+1 and expand.
c.write 11=3+3+2 and expand.
d.write 11=4+4+3 and expand.

Answer 1

@JoeDeWise

Answer 2

here

Answer 3

Okay! I posted my question

Answer 4

114
=11*11*11*11
=114
=14641

Answer 5

So?

Answer 6

I would prefer myself to evaluate powers of 10 or powers of 1 because they are extremely easy.

Answer 7

What do you mean?

Answer 8

for example which one seems easier?
5^4?
10^4?

also c doesn't make sense because 3+3+2 is totally not 11
also 11=4+4+3 seems like it might be harder to use binomial theorem since 4+4+3 consist of 3 terms. But I guess you do binomial again and again to expand (4+4+3)^4.

Answer 9

what do I mean about what?

Answer 10

10^4 seems easier

Answer 11

right

Answer 12

10^4=10000
but 5^4 I would have to go back to multiplying 5*5*5*5 to figure out

Answer 13

Would it be B?

Answer 14

yes in my opinion expanding (10+1)^4 using binomial theorem is tons easier because like I said before evaluating powers of 10 and evaluating powers of 1 are way easy

Answer 15

\[(a+b)^4=a^4+4 \cdot a^3 b+6 \cdot a^2b^2 + 4 \cdot ab^3+b^4 \\ \text{ so } (10+1)^4=10^4+4 \cdot 10^3(1)+6 \cdot 10^2(1)^2+4 \cdot 10(1)^3+1^4\]
try evaluating to see how easy that is

Answer 16

It was B.! Thank you! Could you help me with three more?

Answer 17

I can try

Answer 18

Use Pascal's Triangle to expand the binomial
(d-3)^6

Answer 19

well using pascal's triangle what are the coefficients in the (6+1)th row?

Answer 20

I am unsure

Answer 21

so you don't know where the 7th row is?

Answer 22

I don't understand Pascal's Triangle..

Answer 23

here I wrote 6 rows