Question

Describe the relationship between Pascal’s triangle and the coefficients in front the terms above.

Answer 1

Explanation

An image of pascals triangle which represents the coefficients during expansion.

From the given question, we can see that;

$\begin{gathered} ^0C_0=\frac{0!}{0!0!}=1 \\ ^1C_0=\frac{1!}{1!0!}=1^\text{ and }^1C_1=\frac{1!}{0!1!}=1 \\ ^2C_0=\frac{2!}{2!0!}=1\text{ a}nd\text{ }^{\text{ }2}C_1\text{ =}\frac{2!}{1!1!}=2\text{ }and\text{ }^2C_2=\frac{2!}{0!2!}=1 \end{gathered}$

When we continue in the above manner, we will realize that the given combination in the question matches the coefficients from the pascal triangle