Question

In the expansion of (3a + 4b)^8, which of the following are possible variable terms? Explain your reasoning.
a^2b^3; a^5b^3; ab^8; b^8; a^4b^4; a^8; ab^7; a^6b^5

Answer 1

hint : the degree of each term has to be `8`

Answer 2

\[(a + b)8 = a^8 + 8a^7b + 28a^6b^2 + 56a^5b^3 + 70a^4b^4 + 56a^3b^5 + 28a^2b^6 + 8ab^7 + b^8.\]

Answer 3

for example, `a^2b^3` has degree = `2+3` = 5, which is NOT 8. So this is impossible

Answer 4

so each term that doesn't have a degree of 8 is a variable term?

Answer 5

each term that doesn't have a degree of 8 can NOT be a term in the expansion.

Answer 6

ok, im just a little confused about what the "variable terms" would mean....