JAMB 1991 · UME · Q18

Factorize $1 - (a - b)^2$ .

Worked solution (try it first)

This is a difference of two squares, with $1 = 1^2$ : $1 - (a - b)^2 = [1 - (a - b)][1 + (a - b)]$ .
Remove the inner brackets: $1 - (a - b) = 1 - a + b$ and $1 + (a - b) = 1 + a - b$ .
So the factors are $(1 - a + b)(1 + a - b)$ , option B.