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Factor. $\newline$ $4g^2 - 12g + 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

4g^2 - 12g + 9

Identify Perfect Square Trinomial: Determine if the quadratic can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(ag)^2 - 2abg + b^2$ , where the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms. $\newline$ $4g^2$ is a perfect square, as $(2g)^2 = 4g^2$ . $\newline$ $9$ is a perfect square, as $3^2 = 9$ . $\newline$ The middle term, $-12g$ , is twice the product of the square roots of $4g^2$ and $9$ , since $2 \times 2g \times 3 = 12g$ . $\newline$ Thus, the expression is a perfect square trinomial.
Apply Perfect Square Trinomial Formula: Factor the expression using the perfect square trinomial formula. $\newline$ The factored form of a perfect square trinomial $(ag)^2 - 2abg + b^2$ is $(ag - b)^2$ . $\newline$ For our expression, $ag = 2g$ and $b = 3$ . $\newline$ So, the factored form is $(2g - 3)^2$ .

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