MATH SOLVE

9 months ago

Q:
# Which products result in a difference of squares? Check all that apply.(5z + 3)(–5z – 3)(w – 2.5)(w + 2.5)(8g + 1)(8g + 1)(–4v – 9)(–4v + 9)(6y + 7)(7y – 6)(p – 5)(p – 5)

Accepted Solution

A:

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 squaresIt is required to identify which products result in a difference of 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] It 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 2 and option 4 are correct.Learn more about polynomial here: