Question

Find the middle term of (x-2)^6

Answer 1

Its not there, so it should be zero.

Answer 2

this will be the 4the term
6C3 x^3 (-2)^3

Answer 3

ddo you know how to calculate 6C3 (the number of combination of 3 in 6)?

Answer 4

Thankss for the help. ☺️☺️

Answer 5

yw

Answer 6

The number of terms in the expansion will be 1 more than the power of binomial. In this case, the power is 6, and 6+1=7 so we will have 7 terms all together.

To find the 'middle term' of 7, do (7+1)/2 which equals 4.

So we need to find the 4th term this binomial!

To do this we can use the Binomial Theroem:

To find any term in:\[(a+b)^{n}\]
we can use:

\[t _{k+1}=_{n}C _{k}a ^{n-k}b ^{k}\]

we want \[t _{k+1}=t _{4}\] because we are finding the 4th term, so k must equal 3.

and n will be the power of the binomial

What we have now is:
n=6
k=3
a=x
b=-2

Lets sub it into the formula
\[t _{k+1}=_{n}C _{k}a ^{n-k}b ^{k}\]

\[t _{(3)+1}=_{6}C _{3}x ^{(6-3)}(-2)^{3}=20x ^{3}(-8)=-160x ^{3}\]