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

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Factor quadratics: special cases

Full solution

Q. Factor.

\newline

25j^2 - 10j + 1

Identify Structure: Identify the structure of the quadratic expression; it resembles the form $(a j)^2 - 2 a b j + b^2$ , which factors into $(a j - b)^2$ .
Find $a$ and $b$ : Find $a$ and $b$ such that $(aj)^2 = 25j^2$ and $b^2 = 1$ . Here, $a = 5$ and $b = 1$ because $(5j)^2 = 25j^2$ and $1^2 = 1$ .
Check Middle Term: Check the middle term $-2abj$ to ensure it matches the original expression. $-2 \times 5 \times 1 \times j = -10j$ , which is the middle term of the original expression.
Write Factored Form: Write the factored form using the values of $a$ and $b$ : $(5j - 1)^2$ .

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