Respuesta :
Option second [tex]\rm (w-2.5)(w+2.5)[/tex] and option fourth [tex]\rm (-4v-9)(-4v+9)[/tex] are the products that result in a difference in squares.
It is required to identify which products result in a difference in squares.
What is polynomial?
Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We know that:
[tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
In option first:
[tex]\rm = (5z+3)(-5z-3)\\\rm = -(5z+3)(5z+3)\\\rm = -(5z+ 3)^2[/tex]
Which is not the difference between squares.
In option second:
[tex]\rm=(w-2.5)(w+2.5)\\\rm =(w^2-2.5^2)[/tex]By using [tex]\rm (a^2-b^2)=(a+b)(a-b)[/tex]
It is the difference between squares.
Similarly, in option third:
[tex]\rm =(8g+1)(8g+1)\\\rm =(8g+1)^2[/tex]
It is not the difference between squares.
Similarly, in option forth:
[tex]\rm = (-4v-9)(-4v+9)\\\rm = (4v+9)(4v-9)\\\rm = (4v)^2-9^2[/tex]
It is the difference between squares.
Similarly, in option fifth:
[tex]\rm = (6y+7)(7y-6)\\\rm = 42y^2+13y-42[/tex]
It is not the difference between squares.
Similarly, in option sixth:
[tex]\rm =(p-5)(p-5)\\\rm =(p-5)^2[/tex]
It is also not the difference between squares.
Thus, option second and option fourth are correct.
Learn more about polynomial here:
brainly.com/question/17822016
