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

EXPANSION FOR (3a+4b)^8 IS

6561a^8+69984a^7b+326592a^6b^2+870912a^5b^3+1451520a^4b^4+1548288a^3b^5+1032192a^2b^6+393216ab^7+65536b^8

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

EXPANSION FOR (3a+4b)^8 IS

6561a^8+69984a^7b+326592a^6b^2+870912a^5b^3+1451520a^4b^4+1548288a^3b^5+1032192a^2b^6+393216ab^7+65536b^8

anonymous · Answer

Notice that in every term, the sum of the exponents of a and b is 8. Which of the answers meet this condition?

anonymous · Answer

ab^8; a^8; b^8 @ospreytriple ???

anonymous · Answer

Consider $ab^8$. The exponent of a is 1, and the exponent of b is 8, making the sum of the exponents 9, so it can't be one of the correct choices. Don't forget: just because an exponent isn't written doesn't mean there isn;t one, it is assumed to be 1.

anonymous · Answer

There are other correct choices as well. Remember, the sum of the exponents must be 8.

anonymous · Answer

okay thank you so much :) @ospreytriple

anonymous · Answer

You're welcome