Factor the expression: x^2 + 6x + 9.

Factor the expression: x^2 + 6x + 9.

Step 1: Identify the expression you want to factor, which is x^2 + 6x + 9.
Step 2: Look for a perfect square trinomial. A perfect square trinomial has the form (a + b)^2 = a^2 + 2ab + b^2.
Step 3: In the expression x^2 + 6x + 9, notice that x^2 is a perfect square (it is x^2).
Step 4: Next, identify the middle term, which is 6x. This can be written as 2 * x * 3, where 3 is half of 6.
Step 5: Finally, notice that 9 is also a perfect square (it is 3^2).
Step 6: Since all parts fit the perfect square trinomial form, we can write the expression as (x + 3)(x + 3) or (x + 3)^2.

Factoring Quadratic Expressions – Understanding how to factor quadratic expressions, particularly recognizing perfect square trinomials.
Perfect Square Trinomials – Identifying and applying the formula a^2 + 2ab + b^2 = (a + b)^2.