a) $100x^2 + 20x + 1 = (10x)^2 + 2.10x . 1 + 1 = (10x+1)^2$
b) $a^2 - [5(b-c)]^2 = (a-5b+5c)(a+5b-5c)$
c) $4 - 36x + 81x^2 = 2^2 - 2.2.9x + (9x)^2 = (9x-2)^2$
d) $(x+y)^2 - 2.3.(x+y) + 3^2 = (x+y-3)^2$
e) $a^6-1 = (a^3)^2 - 1 = (a^3-1)(a^3+1) = (a-1)(a^2 + a + 1)(a+1)(a^2 - a + 1) = (a-1)(a+1)(a^2+a+1)(a^2-a+1)$
