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; a6b

Answers are: 
a^5b^3
b^8
a^4b^4
a^8
ab^7
(there are 5 answers)



The exponents for the variable terms must add to 8, which is the original outer exponent of the expression given (3a+4b)^8

For something like a^8, we don't have any other exponent so we don't have to worry about it. If you wanted, you can think of a^8 as a^8b^0 and then note how 8+0 = 8. So the rule still applies

For ab^7, we would write it as a^1b^7 and the rule works here as well (1+7 = 8). 



Something like a^2b^3 is a non-answer because the exponents add to 2+3 = 5
Same goes for ab^8 = a^1b^8 because we have the exponents add to 1+8 = 9
And for a^6b = a^6b^1 we have the sum of exponents being 6+1 = 7

The answer is a because i went through all the other ones that it didn’t come out right