Which of the following is the expansion of (3c + d2)6?
a) 729c6 + 1,458c5d2 + 1,215c4d4 + 540c3d6 + 135c2d8 + 18cd10 + d12
b) 729c6 + 1,458c5d + 1,215c4d2 + 540c3d3 + 135c2d4 + 18cd5 + d6
c) 729c6 + 1,215c5d2 + 810c4d4 + 270c3d6 + 90c2d8 + 15cd10 + d12
d) 729c6 + 243c5d2 + 81c4d4 + 27c3d6 + 9c2d8 + 3cd10 + d12
e) c6 + 6c5d2 + 15c4d4 + 20c3d6 + 15c2d8 + 6cd10 + d12

Option A) is the correct expansion.

Explanation:

on applying binomial theorem,  

Here a=3c, and n=6,

Thus,

⇒

⇒

⇒

⇒

Option (a) is correct.

Step-by-step explanation:

Given :  

We have to expand the given expression and choose the correct from the given options.

Consider the given expression  

Using binomial  theorem ,

We have  

also,

for i = 0 , we have,

for i = 1 , we have,

for i = 2 , we have,

for i = 3 , we have,

for i = 4 , we have,

for i = 5 , we have,

for i = 6 , we have,

Thus, adding all term together, we have,

Thus, Option (a) is correct.

b.an increase in a causes b to decrease

boxplot e is the answer