Question

Use Pascal's Triangle to determine the second term of the expansion of (x - 2)^5

Answer 1

Pascal's triangle up to the 5th iteration is

$\begin{array}{cccccc}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\\1&5&10&10&5&1\end{array}$

This tells us

$(x-2)^5=\boxed{1}x^5(-2)^0+\boxed{5}x^4(-2)^1+\boxed{10}x^3(-2)^2+\boxed{10}x^2(-2)^3+\boxed{5}x^1(-2)^4+\boxed{1}x^0(-2)^5$

so the second term in the expansion is

$5x^4(-2)^1=\boxed{-10x^4}$