1. Expand `4^(th)` term of `(x-2)^6`

Solution:
`(x-2)^6`

`"Here "a=x,b=-2,n=6`

Now, `T_(r+1)=((n),(r))a^(n-r)b^r`

To find `T_4`, we let `r=3`

`:. T_4=T_(3+1)`

`=((6),(3))(x)^3(-2)^3`

`=(6!)/(3!(6-3)!)(x)^3(-2)^3`

`=(6*5*4)/(3*2*1)(x^3)(-8)`

`=20(x^3)(-8)`

`=-160x^3`

So, final answer is
`=-160x^3`

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2. Expand `3^(rd)` term of `(3x-y)^7`

Solution:
`(3x-y)^7`

`"Here "a=3x,b=-y,n=7`

Now, `T_(r+1)=((n),(r))a^(n-r)b^r`

To find `T_3`, we let `r=2`

`:. T_3=T_(2+1)`

`=((7),(2))(3x)^5(-y)^2`

`=(7!)/(2!(7-2)!)(3x)^5(-y)^2`

`=(7*6)/(2*1)(243x^5)(y^2)`

`=21(243x^5)(y^2)`

`=5103x^5y^2`

So, final answer is
`=5103x^5y^2`

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3. Expand `5^(th)` term of `(2x^2-1/x^2)^11`

Solution:
`(2x^2-1/x^2)^11`

`"Here "a=2x^2,b=-1/(x^2),n=11`

Now, `T_(r+1)=((n),(r))a^(n-r)b^r`

To find `T_5`, we let `r=4`

`:. T_5=T_(4+1)`

`=((11),(4))(2x^2)^7(-1/(x^2))^4`

`=(11!)/(4!(11-4)!)(2x^2)^7(-1/(x^2))^4`

`=(11*10*9*8)/(4*3*2*1)(128x^14)(1/(x^8))`

`=330(128x^14)(1/(x^8))`

`=42240x^6`

So, final answer is
`=42240x^6`

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