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
Evaluate the following using binomial theorem:
(999)5
Find the term independent of x in the expansion of
`(x - 2/x^2)^15`
Find the Co-efficient of x11 in the expansion of `(x + 2/x^2)^17`
The constant term in the expansion of `(x + 2/x)^6` is
The last term in the expansion of (3 + √2 )8 is:
Sum of binomial coefficient in a particular expansion is 256, then number of terms in the expansion is:
Expand `(2x^2 -3sqrt(1 - x^2))^4 + (2x^2 + 3sqrt(1 - x^2))^4`
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]
In the binomial expansion of (1 + x)n, the coefficients of the 5th, 6th and 7th terms are in AP. Find all values of n
Choose the correct alternative:
The remainder when 3815 is divided by 13 is
