Number of integral terms in the expansion of (√6 + √10 + √15)^6 is:
A) 3
B) 9
C) 6
D) 10
Hello fardeen_genIn the expansion of , all the terms are in the form , where and .
Now if and , the only terms that have integer values are when and are even. (Note that , but the only way this combines with other even powers is in the term ; i.e. where .)
So:
- if , and there are 4 possible choices
- if , and there are 3 possible choices
- if : 2 choices
- if : 1 choice
Total number of terms, then, is 4+3+2+1 = 10. Answer: D.
Grandad
Hello, fardeen_gen!
A variation of Grandad's explanation . . .
Number of integral terms in the expansion of: is:
. .
In the expansion of ,
. . the terms are of the form: . where
The term will be an integer if are all even.
There are three basic partitions . . .
. . .
Therefore, there are 10 integral terms. (answer D)