First slide

Binomial theorem for positive integral Index

Question

$How many terms are there in the expansion of (4 x + 7 y)^{10} + (4 x - 7 y)^{10} ?$

Easy

A

5
B

6
C

11
D

12

Solution

$(4 x + 7 y)^{10} + (4 x - 7 y)^{10}$
$= [(4 x)^{10} + {}^{10}C_{1} (4 x)^{9} (7 y) + {}^{10}C_{2} (4 x)^{8} (7 y)^{2} + \dots + (7 y)^{10}] - [(4 x)^{10} - {}^{10}C_{1} (4 x)^{9} (7 y) + {}^{10}C_{2} (4 x)^{8} (7 y)^{2} + \dots + (7 y)^{10}]$
$= 2 [{{}^{10}C}_{1}^{} (4 x)^{9} (7 y) + {}^{10}C_{3} (4 x)^{7} + {}^{10}C_{5} (4 x)^{8} (7 y)^{2} + . . + (7 y)^{10}]$
$Therefore, required number of terms = 5 .$

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