Factor by using the perfect-square trinomial formula.
100x^2+20x+1

To factor first multily 100 and 1 and get 100

then find what 2 numbers multiply to get 100 and add to get 20

the numbers are 10 and 10

so
split the center term up
100x^2+10x+10x+1
group
(100x^2+10x)+(10x+1)
undistribute
(10x)(10x+1)+(1)(10x+1)
undistribute/reverse distributive property
(10x+1)(10x+1)
(10x+1)^2

since this is a perfect square problem, the answer will be in the form (ax + b) ^ 2. what can you tell from looking at the original equation? x^2 does not have a coefficient in front of it, so a = 1. the second term is negative, so b must be negative. finally, the last number 100 is the square of + or - 10, so b must be +10 or -10, but we already figured b has to be negative, so b = -10