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 = [tex]\sqrt{9}[/tex] = 3
b² = 1 ⇒ b = [tex]\sqrt{1}[/tex] = 1
and 2ab = 2 × 3 × 1 = 6
Thus
9x² + 6x + 1 = (3x + 1)²
Answer:
(3x + 1)^2
Step-by-step explanation:
The first and last terms are perfect squares. From its structure, this is a perfect square trinomial.
All of the symbols in the expression 9x2 + 6x + 1 are positive, so use the rule for the square of the sum of two terms.
In the given expression, a2 = 9x2 and b2 = 1, so a = 3x and b = 1.
2ab = 2(3x)
= 6x
This result matches the middle term in the polynomial expression, 6x, so apply the rule for the square of the sum of two terms.
The expression 9x2 + 6x + 1 is equal to (3x + 1)2.
