Factor. 25f^2 - 20f + 4 ______

Check Pattern: Determine if the quadratic expression can be factored using the perfect square trinomial formula. A perfect square trinomial is in the form of (a^2 ± 2ab + b^2) = (a ± b)^2. We need to check if 25f^2 - 20f + 4 fits this pattern. 25f^2 is a perfect square, as (5f)^2 = 25f^2. 4 is a perfect square, as 2^2 = 4. The middle term, -20f, should be equal to 2*(5f)*2 if it fits the pattern. Let's check: 2*(5f)*2 = 20f, which matches the middle term except for the sign. Since the middle term is negative, we are looking at a pattern of (a - b)^2.Write Trinomial: Write the expression as a perfect square trinomial. We have identified that 25f^2 - 20f + 4 fits the pattern of a perfect square trinomial (a - b)^2. So, we can write it as (5f - 2)^2.Expand and Confirm: Check the factored form by expanding it to ensure it matches the original expression. Expanding (5f - 2)^2 gives us (5f - 2)(5f - 2) = 25f^2 - 10f - 10f + 4 = 25f^2 - 20f + 4. This matches the original expression, confirming that our factored form is correct.

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

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Algebra 1

Factor quadratics: special cases

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Q. Factor.

\newline

25f^2 - 20f + 4

Check Pattern: Determine if the quadratic expression can be factored using the perfect square trinomial formula. $\newline$ A perfect square trinomial is in the form of $(a^2 \pm 2ab + b^2) = (a \pm b)^2$ . We need to check if $25f^2 - 20f + 4$ fits this pattern. $\newline$ $25f^2$ is a perfect square, as $(5f)^2 = 25f^2$ . $\newline$ $4$ is a perfect square, as $2^2 = 4$ . $\newline$ The middle term, $-20f$ , should be equal to $2*(5f)*2$ if it fits the pattern. $\newline$ Let's check: $2*(5f)*2 = 20f$ , which matches the middle term except for the sign. $\newline$ Since the middle term is negative, we are looking at a pattern of $(a - b)^2$ .
Write Trinomial: Write the expression as a perfect square trinomial. $\newline$ We have identified that $25f^2 - 20f + 4$ fits the pattern of a perfect square trinomial $(a - b)^2$ . $\newline$ So, we can write it as $(5f - 2)^2$ .
Expand and Confirm: Check the factored form by expanding it to ensure it matches the original expression. $\newline$ Expanding $(5f - 2)^2$ gives us $(5f - 2)(5f - 2) = 25f^2 - 10f - 10f + 4 = 25f^2 - 20f + 4$ . $\newline$ This matches the original expression, confirming that our factored form is correct.