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

Mathematics

1 answer:

DanielleElmas [232]3 years ago

4 0

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

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Refer to problem 7. In this case, adding any two adjacent angles together forms a straight line.