Given:
[tex]25m^2-10m+1[/tex]Let's factor the expression.
To factor the expression, first rewrite 5² = 25:
[tex]\begin{gathered} 5^2m^2-10m+1 \\ \\ (5m)^2-10m+1 \end{gathered}[/tex]Now, rewrite 1² = 1:
[tex](5m)^2-10m+1^2[/tex]Now, check that the middle term is two times the product of the first term being squared (5m) and the last term (1).
We have:
2 x (5m x 1) = 10 m
Thus, we have the expression:
[tex](5m)^2-2*5m*1+1^2[/tex]Now, factor using the Perfect Square Trinomial rule:
[tex]a^2-2ab+b^2=(a-b)^2[/tex]Thus, we have:
[tex](5m)^2-2*5m*1+1^2=(5m-1)^2[/tex]Where:
• a = 5m
,• b = 1
Therefore, the factored form of the given expression is:
[tex](5m-1)^2[/tex]ANSWER:
[tex](5m-1)^2[/tex]