Question

Question 6 Using Binomial Theorem, evaluate (96)^3

Class X1 - Maths -Binomial Theorem Page 167

Answer 1

(96)³
= (100 - 4)³
use the formula,
(x - y)^n = nC0.x^n - nC1.x^(n-1)y + nC2.x^(n-2)y^2 +........(-1)^n.nCn.y^n

= 3C0.(100)^3 - 3C1.(100)^2.4 + 3C2.(100)(4)^2 - 3C3.(4)^3

= 3C0.(10^2)^3 - 3C1.(10^2)^2.4 + 3C2.(10^2)(4)^2 - 3C3.(4)^3

= {3!/3!}.10^6 - {3!/2!}.(10^4)×4 + {3!/2!}(10^2)×16 - {3!/3!}(4)^3

= 10^6 - 3 × 10^4 × 4 + 3 × 10^2 × 16 - 64

= 10^6 - 12 × 10^4 + 48 × 10^2 - 64

= 1000000 + 4800 - ( 120000 + 64)

= 1004800 - 120064

= 884736