By definition, a Perfect square is a number that is the square of an Integer.
In this case, you have the following expression given in the exercise:
[tex]169-4d^2[/tex]You can identify that:
[tex]169=13\cdot13=13^2[/tex]Therefore, it is a Perfect square.
Notice that:
[tex]4d^2=(2d)^2[/tex]Therefore, it is a Perfect square.
For this case you must apply the Difference of two squares is:
[tex]a^2-b^2=(a+b)(a-b)[/tex]Then, you can factor the expression:
[tex]=-(2d-13)(2d+13)[/tex]The answers are:
- Factored expression:
[tex]-(2d-13)(2d+13)[/tex]- ´Perfect squares:
[tex]\begin{gathered} 169=13^2 \\ 4d^2=(2d)^2 \end{gathered}[/tex]
