Question

How do you find the eight term in the expansion `(a + b)^14`?

Answer 1

`3432a^7b^7`

Explanation:

If you have not had much to do with Binomial Expansion, Khan Academy have a great video that simplifies the process:

https://www.khanacademy.org/math/algebra2/polynomial-functions/binomial-theorem/v/binomial-theorem

Consider the formula used to expand a Binomial Equation:
`sum_(k=0)^(n)*^nC_k*a^(n-k)*b^k`

Where:
`n` is the power to which the equation is raised.

Therefore, if we consider your equation:
`(a+b)^14`

From your equation, we can see that the power to which the equation is raised to is: 14.

Before we have a look at the 8th term, let's have a look at the first term so we can observe the relationship between the Binomial Theory and the subsequent expansion:

For the first term of: `(a+b)^14`

`sum_(k=0)^(n)*^nC_k*a^(n-k)*b^k`
`=^(14)C_0*a^14*b^0`
`=1*a^14*1`
`=a^14`

Now let's have a look at expanding the 8th Term of the equation:

`sum_(k=0)^(n)*^nC_k*a^(n-k)*b^k`
`=^(14)C_7*a^7*b^7`
`=3432*a^7*b^7`
`=3432a^7b^7`