Question

factor the special product
25s^2-10s+1

Answer 1

(ax + b)² =
a²x² + 2abx + b²

25s² - 10s + 1 is in that form, so we just need to identify the constants a and b.

Looking at the second degree term in the equations, we see how a² must = 25.
Then a = 5.

Looking at the second term in each, we see how 2ab must = -10
Pluggin in the known value for a,

2*5*b = -10
Dividing by 10,
b = -1

So a = 5 and b = -1. Now we just plug back into the special case!
(ax + b)²

(5x - 1)² is your answer.
With practice, you'll be able to see patterns like this immediately without all this work.

Answer 2

(5x - 1)²
^-- x in that should be s, my bad.
(5s - 1)² is the answer.