In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5

I know they have to add up to 8, & I know ab7 is one, but what are the others?

Question

In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning.
a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b5

I know they have to add up to 8, & I know ab7 is one, but what are the others?

tkhunny · Answer

The degree of the term had better be 8.  You have 5, 8, 9, 8, 8, 8, 8, 11

How did you determine that ab^7 is degree 8?

anonymous · Answer

Ohhh I get it, I accidentally added b and 7. So ab7 isnt one of the options?

tkhunny · Answer

ab^7 IS degree 8.  Why is this so?

anonymous · Answer

because b = 1?

anonymous · Answer

And I added b and 7

tkhunny · Answer

b is not 1.  That makes no sense at all.

ab^7 is the same as a^1 * b^7.  Add the 1 and the 7 exponents and you get 8.  Candidate!
a^6 * b^5 Add the 6 and the 5 exponents and you get 11.  NOT a candidate!