For what value of m xy²m = (2xy + 5y)²-(2xy-5y)²

The equation you provided is: xy²m = (2xy + 5y)²-(2xy-5y)²

Let's simplify the right side of the equation first:

(2xy + 5y)² - (2xy - 5y)²

This is a difference of squares, which can be simplified to:

[(2xy + 5y) + (2xy - 5y)] * [(2xy + 5y) - (2xy - 5y)]

Simplify the terms in the brackets:

[4xy] * [10y]

This simplifies to:

40xy²

So, the original equation simplifies to:

xy²m = 40xy²

Divide both sides by xy² (assuming that xy² ≠ 0):

m = 40

So, the value of m that satisfies the equation is m = 40.