Factor. 25x^2 - 10x + 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 (ax)^2 - 2abx + b^2, which factors to (ax - b)^2. Check if 25x^2 - 10x + 1 fits this pattern. 25x^2 can be written as (5x)^2, and 1 can be written as 1^2. The middle term, -10x, should be equal to 2 times the product of the square roots of the first and last terms if it's a perfect square trinomial. 2 * 5x * 1 = 10x, which matches the middle term except for the sign. So, 25x^2 - 10x + 1 is a perfect square trinomial.Factor Trinomial: Factor the perfect square trinomial. Since we have identified that 25x^2 - 10x + 1 is a perfect square trinomial, it can be factored as: (5x)^2 - 2 * 5x * 1 + 1^2 = (5x - 1)^2

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

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25x^2 - 10x + 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 $(ax)^2 - 2abx + b^2$ , which factors to $(ax - b)^2$ . $\newline$ Check if $25x^2 - 10x + 1$ fits this pattern. $\newline$ $25x^2$ can be written as $(5x)^2$ , and $1$ can be written as $1^2$ . $\newline$ The middle term, $-10x$ , should be equal to $2$ times the product of the square roots of the first and last terms if it's a perfect square trinomial. $\newline$ $2 \times 5x \times 1 = 10x$ , which matches the middle term except for the sign. $\newline$ So, $25x^2 - 10x + 1$ is a perfect square trinomial.
Factor Trinomial: Factor the perfect square trinomial. $\newline$ Since we have identified that $25x^2 - 10x + 1$ is a perfect square trinomial, it can be factored as: $\newline$ $(5x)^2 - 2 \times 5x \times 1 + 1^2 = (5x - 1)^2$