Factor. 4v^2 - 12v + 9 ______

Check Perfect Square Trinomial: Determine if the quadratic 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. The given quadratic is 4v^2 - 12v + 9. We can check if 4v^2 is a perfect square, which it is since (2v)^2 = 4v^2. We can check if 9 is a perfect square, which it is since 3^2 = 9. We can check if -12v is twice the product of the square roots of 4v^2 and 9, which it is since 2 * 2v * 3 = 12v. So, the quadratic is a perfect square trinomial.Write in Correct Form: Write the quadratic in the form of (a^2 ± 2ab + b^2). The given quadratic is already in this form: (2v)^2 - 2 * 2v * 3 + 3^2.Factor Using Formula: Factor the quadratic using the perfect square trinomial formula. Since we have a minus sign in the middle term, we will use the formula (a - b)^2 = a^2 - 2ab + b^2. The factored form is (2v - 3)^2.

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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4v^2 - 12v + 9

Check Perfect Square Trinomial: Determine if the quadratic can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form $(a^2 \pm 2ab + b^2)$ , which factors to $(a \pm b)^2$ . $\newline$ The given quadratic is $4v^2 - 12v + 9$ . $\newline$ We can check if $4v^2$ is a perfect square, which it is since $(2v)^2 = 4v^2$ . $\newline$ We can check if $9$ is a perfect square, which it is since $3^2 = 9$ . $\newline$ We can check if $-12v$ is twice the product of the square roots of $4v^2$ and $9$ , which it is since $(a \pm b)^2$ $0$ . $\newline$ So, the quadratic is a perfect square trinomial.
Write in Correct Form: Write the quadratic in the form of $(a^2 \pm 2ab + b^2)$ . $\newline$ The given quadratic is already in this form: $(2v)^2 - 2 \times 2v \times 3 + 3^2$ .
Factor Using Formula: Factor the quadratic using the perfect square trinomial formula. $\newline$ Since we have a minus sign in the middle term, we will use the formula $(a - b)^2 = a^2 - 2ab + b^2$ . $\newline$ The factored form is $(2v - 3)^2$ .