Question

What is the factored form of the expression 9x2 + 6x + 1?

Answer 1

Answer:

(3x + 1)²

Step-by-step explanation:

Given

9x² + 6x + 1 ← is a perfect square of the form

(ax + b)² = a²x² + 2abx +  b²

Compare like terms to find a and b

a²x² = 9x² ⇒ a² = 9 ⇒ a = $\sqrt{9}$ = 3

b² = 1 ⇒ b = $\sqrt{1}$ = 1

and 2ab = 2 × 3 × 1 = 6

Thus

9x² + 6x + 1 = (3x + 1)²