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