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Factor. $\newline$ $25h^2 - 10h + 1$

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Factor quadratics: special cases

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Q. Factor.

\newline

25h^2 - 10h + 1

Check for 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 of $(a^2 \pm 2ab + b^2)$ which factors to $(a \pm b)^2$ . $\newline$ $25h^2 - 10h + 1$ can be written as $(5h)^2 - 2\cdot(5h)\cdot1 + 1^2$ , which resembles the perfect square trinomial formula.
Apply Perfect Square Trinomial Formula: Factor the expression using the perfect square trinomial formula. $\newline$ Since $25h^2$ is a perfect square of $(5h)^2$ and $1$ is a perfect square of $1^2$ , and the middle term is twice the product of $5h$ and $1$ , we can write the expression as: $\newline$ $(5h - 1)^2$

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