Super quick question!?

Question

In the expansion of (a+b)^8, what is the value of the exponent, k, in the term that contains, (a^5)(b^k)?

a) 5
b) 56
c) 4
d) 3

Answer 1

The exponents need to add to 8.

So, if you have a^5, then you have b^(8-5) = b^3

So, k = 3

Answer 2

3

Answer 3

The coefficients of the expansion will be:
1, 8, 28, 56, 70, 56, 28, 8, 1

Starting off at column zero and counting out to column 5, you get 56. The value 56 will be in column 3 coming back the other way, so it's power value will be three.

→(a^5)(b^3)

Answer 4

This one's so easy, you should do it yourself.

Try (a+b)^2. What do you notice about the powers of a and b in each of the terms?

Now try (a+b)^3. Do you see a pattern developing?

You could try (a+b)^4 if you don't see it yet.

Answer 5

binomial expansion yields each term as
nCm*x^(n-m)*y^k....
so accordingly here,
n=8,
m=5....
so here k would be(8-5)=3..

Answer 6

c) 4