How many terms are in the expansion (x + y)^10

Question

katherinesmith · Answer

1024?

katherinesmith · Answer

10
		
13
		
12
		
11

are my options

raden · Answer

sorry, my mistake. that was to determine the sum all coefficients :)
now there are (n+1) terms, here n = 10
so, it is (10+1) terms = 11 terms

katherinesmith · Answer

can you help me with another?

raden · Answer

i'll try

katherinesmith · Answer

what is the 4th term of $$(a-\sqrt{2})^{8}$$

raden · Answer

it can be :
8C3 (a)^(8-4) (-sqrt(2))^3 then evaluate the calculation

raden · Answer

opsss..  i mean
8C3 (a)^(8-3) (-sqrt(2))^3

raden · Answer

you know about combination, right ?

raden · Answer

use the formula :
nCr = n!/(r!(n-r)!)
so, to get the exact value of 8C3, it means n=8, and r=3
8C3 = 8!/(3!(8-3)!) = 8!/(3!5!) = (8.7.6.5!)/(3.2.1.5!)
cancel the 5!'s, then simplify again :
= 8.7.6/3.2.1
= 56

raden · Answer

now for (-sqrt(2))^3.
= (-sqrt(2)) * (-sqrt(2)) * (-sqrt(2))
= - 2 sqrt(2)

raden · Answer

therefore, the 4th term of 8C3 (a)^(8-3) (-sqrt(2))^3 is 
= 56 (a)^5 ( - 2 sqrt(2))
= - 112 sqrt(2) a^5