Question

(x-1)²-25=0
Factor by using the difference between two squares

Answer 1

The answer are x=-4, x=6. I guess

Answer 2

see explanation

Explanation:

A difference of 2 squares factors in general as

a² - b² = (a - b)(a + b)

(x - 1)² - 25 ← is a difference of squares

with a = x - 1 and b = 5, thus

(x - 1)² - 25

=(x - 1 - 5)(x - 1 + 5) = (x - 6)(x + 4), then

(x - 6)(x + 4) = 0

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 4 = 0 ⇒ x = - 4

Solutions are x = - 4, x = 6