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Factor. $\newline$ $25j^2 - 30j + 9$

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Factor quadratics: special cases

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Q. Factor.

\newline

25j^2 - 30j + 9

Check 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 $(a^2 \pm 2ab + b^2) = (a \pm b)^2$ . We need to check if $25j^2 - 30j + 9$ fits this pattern. $\newline$ $25j^2$ is a perfect square, as it is $(5j)^2$ . $\newline$ $9$ is a perfect square, as it is $3^2$ . $\newline$ The middle term, $-30j$ , is twice the product of $5j$ and $3$ , which is $-2 \times 5j \times 3 = -30j$ . $\newline$ So, the expression is a perfect square trinomial.
Factor Using Formula: Factor the expression using the perfect square trinomial formula. $\newline$ Since we have identified that $25j^2 - 30j + 9$ is a perfect square trinomial, we can write it as: $\newline$ $(5j)^2 - 2 \times 5j \times 3 + 3^2$ $\newline$ This fits the pattern $(a^2 - 2ab + b^2) = (a - b)^2$ . $\newline$ Therefore, the factored form is $(5j - 3)^2$ .

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