Question

factor completely.
25j² + 10j + 1

Explanation:

Step1: Identify the form

The quadratic \(25j^{2}+10j + 1\) is a perfect square trinomial. The general form of a perfect square trinomial is \(a^{2}+2ab + b^{2}=(a + b)^{2}\).
Here, \(a^{2}=25j^{2}\), so \(a = 5j\) (since \((5j)^{2}=25j^{2}\)). And \(b^{2}=1\), so \(b = 1\) (since \(1^{2}=1\)).

Step2: Check the middle term

Now, check the middle term \(2ab\). Substitute \(a = 5j\) and \(b = 1\) into \(2ab\), we get \(2\times(5j)\times1=10j\), which matches the middle term of the given quadratic.

Step3: Factor the quadratic

Using the formula for a perfect square trinomial \(a^{2}+2ab + b^{2}=(a + b)^{2}\), with \(a = 5j\) and \(b = 1\), we factor \(25j^{2}+10j + 1\) as \((5j + 1)^{2}\).

Answer:

\((5j + 1)^{2}\)