Question

Insert a monomial so that the result is an identity.

(5x+...)(5x-...)=25x^2-0.16y^4

Answer 1

To make the expression (5x+...)(5x-...) equal to 25x^2-0.16y^4, you need to insert the monomial -0.16y^4 in place of the ellipses.

Step-by-step explanation:

To make the expression (5x+...)(5x-...) equal to 25x^2-0.16y^4, we need to insert a monomial in place of the ellipses. We can find this monomial by expanding the left side of the equation and comparing it to the right side.

1. Expand the expression (5x+...)(5x-...): (5x+...)(5x-...) = 25x^2 - ...
2. Compare the expanded expression to the right side of the equation: 25x^2 - ... = 25x^2 - 0.16y^4
3. From the comparison, we can see that the monomial we need to insert is -0.16y^4

Therefore, the expression (5x+...)(5x-...) can be written as (5x-0.16y^4)(5x-0.16y^4) in order for the result to be equal to 25x^2-0.16y^4.