Respuesta :
The product of the two algebraic expression is a way to multiply these variables, coefficient and constants with each other. For the option 2 and 4 the result of the function is difference of the squares. Thus the option 2 and 4 are correct options.
Product of the algebraic expression-
Algebraic expression is a combination of the variables and coefficients. The product of the two algebraic expression is a way to multiply these variables, coefficient and constants with each other.
Given information-
1) The equation given in the option 1 is,
[tex](5z+3)(-5z-3)=-(5z+3)(5z+3)[/tex]
[tex](5z+3)(-5z-3)=-(5z+3)^2[/tex]
The result is not the difference of the square. Thus the option 1 is not correct.
2) The equation given in the option 2 is,
[tex](w-2.5)(w+2.5)[/tex]
In the algebra,
[tex](a+b)(a-b)=a^2-b^2[/tex]
Use this formula for the above equation we get,
[tex](w-2.5)(w+2.5)=w^2-(2.5)^2[/tex]
The result is the difference of the square. Thus the option 2 is correct.
3) The equation given in the option 3 is,
[tex](8g+1)(8g+1)=(8g+1)^2[/tex]
The result is not the difference of the square. Thus the option 3 is not correct.
4) The equation given in the option 4 is,
[tex](-4v-9)(-4v+9)=-(4v+9)[-(4v-9)][/tex]
[tex](-4v-9)(-4v+9)=(4v+9)(4v-9)[/tex]
[tex](-4v-9)(-4v+9)=4v^2-9^2[/tex]
The result is the difference of the square. Thus the option 4 is correct.
5) The equation given in the option 5 is,
[tex](6y+7)(7y-6)=42y^2+13y-42[/tex]
The result is not the difference of the square. Thus the option 5 is not correct.
6) The equation given in the option 6 is,
[tex](p-5)(p-5)=(p-5)^2[/tex]
[tex](5z+3)(-5z-3)=-(5z+3)^2[/tex]
The result is not the difference of the square. Thus the option 6 is not correct.
Hence for the option 2 and 4 the result of the function is difference of the squares. Thus the option 2 and 4 are correct options.
Learn more about the product of the algebraic expression here;
https://brainly.com/question/17312
