Factor. 9q^2 + 12q + 4 ______

Check Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. A perfect square trinomial is in the form (a^2 + 2ab + b^2) which factors to (a + b)^2. We can check if 9q^2 + 12q + 4 is a perfect square trinomial by identifying a^2, 2ab, and b^2 in the expression. 9q^2 is a perfect square since (3q)^2 = 9q^2. 4 is a perfect square since 2^2 = 4. The middle term, 12q, should be equal to 2ab, where a = 3q and b = 2. Let's check if 2ab = 12q: 2 * 3q * 2 = 6q * 2 = 12q. Since all conditions for a perfect square trinomial are met, we can proceed to factor it.Identify Factors: Factor the perfect square trinomial using the formula (a + b)^2. Since we have identified a = 3q and b = 2, we can write the expression as (3q + 2)^2. Therefore, the factored form of 9q^2 + 12q + 4 is (3q + 2)(3q + 2) or (3q + 2)^2.

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Factor quadratics: special cases

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Q. Factor.

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9q^2 + 12q + 4

Check Perfect Square Trinomial: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(a^2 + 2ab + b^2)$ which factors to $(a + b)^2$ . $\newline$ We can check if $9q^2 + 12q + 4$ is a perfect square trinomial by identifying $a^2$ , $2ab$ , and $b^2$ in the expression. $\newline$ $9q^2$ is a perfect square since $(3q)^2 = 9q^2$ . $\newline$ $4$ is a perfect square since $2^2 = 4$ . $\newline$ The middle term, $(a + b)^2$ $0$ , should be equal to $2ab$ , where $(a + b)^2$ $2$ and $(a + b)^2$ $3$ . $\newline$ Let's check if $(a + b)^2$ $4$ : $(a + b)^2$ $5$ . $\newline$ Since all conditions for a perfect square trinomial are met, we can proceed to factor it.
Identify Factors: Factor the perfect square trinomial using the formula $(a + b)^2$ . Since we have identified $a = 3q$ and $b = 2$ , we can write the expression as $(3q + 2)^2$ . Therefore, the factored form of $9q^2 + 12q + 4$ is $(3q + 2)(3q + 2)$ or $(3q + 2)^2$ .