First slide

Binomial theorem for positive integral Index

Question

The value of $\frac{19^{3} + 6^{3} + (3) (19) (6) (25)}{3^{6} + 6 (243) (2) + (15) (81) (4) + (20) (27) (8) + 15 (9) (16) + 6 (3) (32) + 64}$ is

Easy

A

19
B

6
C

25
D

1

Solution

Numerator $= 19^{3} + 6^{3} + 3 (19) (6) (19 + 6)$
$= (19 + 6)^{3} = 25^{3}$
and denominator $= (3 + 2)^{6} = 5^{6}$
Thus, given expression = 1

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