Answer: C. (5x+3)(5x+3)
Step-by-step explanation:
This is assuming this is a quadratic with 25x2 actually being 25x^2
We can start by simplifying the 25 to be 5^2
As well as the 9 to be 3^2
The expression now looks like: [tex]5^{2}x^{2} + 30x + 3^2[/tex]
Now we can apply an exponent rule to the 5^2 x^2
The rule states: [tex]a^{m}b^{m} = (ab)^m[/tex]
So this means: [tex]5^{2}x^{2} = (5x)^2[/tex]
We can now rewrite 30x as 2 * 5x * 3
The expression now looks like: [tex](5x)^{2} + 2 * 5x * 3 + 3^{2}[/tex]
Now this expression matches with the perfect square formula which states:
[tex](a+b)^{2} = a^{2} +2* a * b + b^{2}[/tex]
Our a value is 5x and our b value is 3.
So: [tex](a+b)^{2} = (5x+3)^{2}[/tex]
The answer is (5x+3)(5x+3)
