Factor the expression 4x^2 - 12x + 9.

Factor the expression 4x^2 - 12x + 9.

Step 1: Identify the expression you want to factor: 4x^2 - 12x + 9.
Step 2: Check if the expression is a perfect square trinomial. A perfect square trinomial has the form (a - b)^2 = a^2 - 2ab + b^2.
Step 3: Identify 'a' and 'b' in the expression. Here, a^2 = 4x^2, so a = 2x. Also, b^2 = 9, so b = 3.
Step 4: Calculate -2ab. Here, -2ab = -2 * (2x) * (3) = -12x, which matches the middle term of the expression.
Step 5: Since the expression matches the form of a perfect square trinomial, we can write it as (2x - 3)(2x - 3).
Step 6: Simplify the expression to (2x - 3)^2.

Factoring Quadratic Expressions – The process of rewriting a quadratic expression as a product of its factors.
Perfect Square Trinomials – Recognizing and factoring expressions that can be expressed as the square of a binomial.