Question

Factor 9y2 - 12y + 4.

(3 y - 2)(3 y + 2)
(3 y - 4)( y + 1)
(3 y - 2) 2

Answer 1

(y - 2)²

Explanation:

9y² - 12y + 4 ← is a perfect square of the form

(ax - b)² = a²x² - 2abx + b²

Compare like terms with 9y² - 12y + 4, thus

a² = 9 ⇒ a = 3

b² = 4 ⇒ b = 2 and

- 2ab = - 2 × 3 × 2 = - 12

Thus

9y² - 12y + 4 = (3y - 2)²