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Factor. $\newline$ $25m^2 - 20m + 4$

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Factor quadratics: special cases

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Q. Factor.

\newline

25m^2 - 20m + 4

Check Perfect Square Trinomial: Determine if the quadratic expression can be factored as a perfect square trinomial. $\newline$ A perfect square trinomial is in the form $(a + b)^2 = a^2 + 2ab + b^2$ . We need to check if $25m^2 - 20m + 4$ fits this pattern. $\newline$ $25m^2$ is a perfect square, as it is $(5m)^2$ . $\newline$ $4$ is a perfect square, as it is $2^2$ . $\newline$ The middle term, $-20m$ , should be equal to $2*(5m)*2$ if the expression is a perfect square trinomial. $\newline$ Let's check: $2*(5m)*2 = 20m$ , but our middle term is $-20m$ , so it matches the pattern with a negative sign.
Write as Perfect Square: Write the expression as a perfect square trinomial. $\newline$ Since the expression matches the pattern of a perfect square trinomial, we can write it as: $\newline$ $(5m - 2)^2 = (5m)^2 - 2\times(5m)\times2 + 2^2$ $\newline$ This matches our original expression $25m^2 - 20m + 4$ .
Factor as Binomial Square: Factor the expression as the square of a binomial. $\newline$ The factored form of the expression is $(5m - 2)^2$ .

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