Question

factor. 25w^{2}-10w + 1

Explanation:

Step1: Recognize the form

This is a quadratic trinomial of the form $ax^{2}+bx + c$, where $a = 25$, $b=-10$, $c = 1$. Notice that it may be a perfect - square trinomial. The formula for a perfect - square trinomial is $(m - n)^2=m^{2}-2mn + n^{2}$.

Step2: Identify $m$ and $n$

For $25w^{2}-10w + 1$, we have $m^{2}=25w^{2}$, so $m = 5w$ (since $\sqrt{25w^{2}}=5w$), and $n^{2}=1$, so $n = 1$. Also, $2mn=2\times(5w)\times1 = 10w$.

Step3: Factor

Using the perfect - square trinomial formula $(m - n)^2=m^{2}-2mn + n^{2}$, we can factor $25w^{2}-10w + 1$ as $(5w - 1)^2$.

Answer:

$(5w - 1)^2$