Number of integral terms in the expansion of (√6 + √10 + √15)^6 is:

A) 3

B) 9

C) 6

D) 10

- Feb 13th 2009, 10:31 PMfardeen_genNumber of integral terms in the expansion of (√6 + √10 + √15)^6 is?
Number of integral terms in the expansion of (√6 + √10 + √15)^6 is:

A) 3

B) 9

C) 6

D) 10 - Feb 14th 2009, 05:43 AMGrandadIntegral terms
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

- Feb 14th 2009, 12:12 PMSoroban
Hello, fardeen_gen!

A variation of Grandad's explanation . . .

Quote:

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)