4. Expand (x - 2)5

We use the binomial theorem

(x - 2)5 = x5 + 5x4(-2) + 10x3(-2)2 + 10x2(-2)3 + 5x(-2)4 + (-2)5

First compute the powers.

= x5 + 5x4(-2) + 10x3(4) + 10x2(-8) + 5x(16) + (-32)

then multiply the numerical factors in each term.

= x5 - 10x4 + 40x3 - 80x2 + 80x - 32