Question

find the 15th term of (x+2y)^20, where x^20 is labeled as the 0th term.

Answer 1

Do you know the formula for binomial expansion?

Answer 2

yes

Answer 3

so for finding nth term in a binomial expansion you use the following formula

\[nC _{r-1}a ^{n-(r-1)}b ^{(r-1)}\]

Answer 4

Or PASCAL'S TRIANGLE

Answer 5

r the no. of the term you are trying to find and n is the power of the expansion

So for this problem n = 20 and r = 15

Answer 6

\[20C _{14} X ^{(20-14)} (2Y)^{14}\]

Answer 7

\[20C _{14} X ^{6} (2Y)^{14}\]

Answer 8

Can you find the value?

Answer 9

no, i messed up somewhere.

Answer 10

can you guide me through the next steps?

Answer 11

how do you find\[20C _{14}\] ??

Answer 12

20!/r!(n-r)!

Answer 13

20!/14!(6)!

Answer 14

easier way is the difference between 20 and 14 is 6 right. so you have to write it like this\[\frac{ 20 \times 19 \times 18 \times 17 \times 16 \times 15 }{ 1 \times 2 \times 3 \times 4 \times 5 \times 6 }\]

Numerator 6 nos. starting from 20 multiplied

and

denominator 6 nos. starting from 1 multiplied.

Now you simplify this fraction

Answer 15

what you wrote will be the same too

Answer 16

38760?

Answer 17

now you have 20C 14. The nest term x^6 can't do anything to it so leave it as it is.

next term (2y) ^14 = 2^14 y ^14. You can find what 2^14 using calculator.

Multiply the answer with what you get for 20C14. That will be your numerical part. Then you will have x^6 y^14 next to it.

Answer 18

yes 38760

Answer 19

then find 2^14

Answer 20

2^14=16384

Answer 21

38760*16384*x^6*y^14

Answer 22

38760* 16384

Answer 23

multiply the numbers and write as one

Answer 24

635043840*x^6*y^14

Answer 25

yes

Answer 26

thats it?

Answer 27

yes

Answer 28

thanks

Answer 29

that will be your 15th term