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Factor. $\newline$ $9x^2 + 12x + 4$

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Factor quadratics: special cases

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Q. Factor.

\newline

9x^2 + 12x + 4

Determine Factoring Possibility: Determine if the quadratic expression can be factored using the standard form $ax^2 + bx + c$ . The given expression is already in the standard form, where $a = 9$ , $b = 12$ , and $c = 4$ .
Check Perfect Square Trinomial: Check if the expression is a perfect square trinomial. A perfect square trinomial is in the form $(ax)^2 + 2abx + b^2$ , which factors to $(ax + b)^2$ . In this case, $(3x)^2 + 2(3x)(2) + 2^2 = 9x^2 + 12x + 4$ , so it is a perfect square trinomial.
Factor Perfect Square Trinomial: Factor the perfect square trinomial. $\newline$ Since $9x^2 + 12x + 4$ is a perfect square trinomial, it factors to $(3x + 2)^2$ .

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