Factor 144f^2 - 24f + 1

(12f - 1) ²

Step-by-step explanation:

Consider the factors of the product of the f² term and the constant term which sum to give the coefficient of the f-term

product = 144 * 1 = 144, sum = - 12

The factors are - 12 and - 12

Use these factors to split the middle term

144f² - 12f - 12f + 1 (factor the first/second and third/fourth terms)

12f (12f - 1) - 1 (12f - 1) ← factor out (12f - 1)

= (12f - 1) (12f - 1) = (12f - 1) ²