Binomial Expansion

In a materials science laboratory, the expansion factor of a synthetic polymer $P$ relative to temperature change $t$ is modeled by the function:

\left(2 + \frac{kt}{4}\right)^5

where $k$ is a non-zero constant.

Find the first 4 terms, in ascending powers of $t$ , of the binomial expansion of $P (t)$ . Give each term in its simplest form.

[4]

To account for sensor drift, a corrected expansion model $R (t)$ is defined as:

R (t) = (5 + 3 t) P (t)

Given that in the expansion of $R (t)$ , the coefficient of the $t$ term is equal to the constant term, determine the value of $k$ .

[4]

Binomial Expansion Questions

In a materials science laboratory, the expansion factor of a synthetic polymer $P$ relative to temperature change $t$ is modeled by the function:

\left(2 + \frac{kt}{4}\right)^5

where $k$ is a non-zero constant.

Find the first 4 terms, in ascending powers of $t$ , of the binomial expansion of $P (t)$ . Give each term in its simplest form.

[4]

To account for sensor drift, a corrected expansion model $R (t)$ is defined as:

R (t) = (5 + 3 t) P (t)

Given that in the expansion of $R (t)$ , the coefficient of the $t$ term is equal to the constant term, determine the value of $k$ .

[4]