Advertisements
Advertisements
प्रश्न
Expand the following by using binomial theorem.
(2a – 3b)4
Advertisements
उत्तर
(x + a)n = nC0 xn a0 + nC1 xn-1 a1 + nC2 xn-2 a2 +...+ nCr xn-r ar +...+ nCn an
∴ (2a - 3b)4 = 4C0 (2a)4 - 4C1 (2a)3 (3b)1 + 4C2 (2a)2 (3b)2 - 4C3 (2a)1 (3b)3 + 4C4 (3b)4
`= 1 xx 2^4 "a"^4 - (4) 2^3 "a"^3 (3"b") + (4 xx 3)/(2 xx 1) 2^2 "a"^2 3^2 "b"^2 - (4 xx 3 xx 2)/(3xx2xx1) (2"a")3^3 "b"^3 + 1(3^4"b"^4)`
= 16a4 - 96a3b + 216a2b2 - 216ab3 + 81b4
APPEARS IN
संबंधित प्रश्न
Expand the following by using binomial theorem.
`(x + 1/y)^7`
Find the middle terms in the expansion of
`(x + 1/x)^11`
Find the middle terms in the expansion of
`(3x + x^2/2)^8`
Find the term independent of x in the expansion of
`(x^2 - 2/(3x))^9`
Show that the middle term in the expansion of is (1 + x)2n is `(1*3*5...(2n - 1)2^nx^n)/(n!)`
The middle term in the expansion of `(x + 1/x)^10` is
Compute 1024
Using binomial theorem, indicate which of the following two number is larger: `(1.01)^(1000000)`, 10
Find the coefficient of x4 in the expansion `(1 + x^3)^50 (x^2 + 1/x)^5`
If a and b are distinct integers, prove that a − b is a factor of an − bn, whenever n is a positive integer. [Hint: write an = (a − b + b)n and expaand]
