Factor. 16v^2 - 8v + 1 ______

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. Check if 16v^2 - 8v + 1 fits this pattern. 16v^2 is a perfect square, as (4v)^2 = 16v^2. 1 is a perfect square, as (1)^2 = 1. The middle term, -8v, is twice the product of 4v and 1, as 2 * 4v * 1 = 8v. So, 16v^2 - 8v + 1 is a perfect square trinomial.Factor Using Formula: Factor the perfect square trinomial using the formula (a^2 - 2ab + b^2) = (a - b)^2. Here, a = 4v and b = 1. (16v^2 - 8v + 1) = (4v - 1)^2

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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16v^2 - 8v + 1

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 $(a \pm b)^2$ . $\newline$ Check if $16v^2 - 8v + 1$ fits this pattern. $\newline$ $16v^2$ is a perfect square, as $(4v)^2 = 16v^2$ . $\newline$ $1$ is a perfect square, as $(1)^2 = 1$ . $\newline$ The middle term, $-8v$ , is twice the product of $4v$ and $1$ , as $(a \pm b)^2$ $0$ . $\newline$ So, $16v^2 - 8v + 1$ is a perfect square trinomial.
Factor Using Formula: Factor the perfect square trinomial using the formula $(a^2 - 2ab + b^2) = (a - b)^2$ . $\newline$ Here, $a = 4v$ and $b = 1$ . $\newline$ $(16v^2 - 8v + 1) = (4v - 1)^2$