To find the product of (4x-5y)^2, we can rewrite the problem as: (4x-5y)(4x-5y) (two times because it is squared)
Now, time to use that old method we learned in middle school: FOIL. (Firsts, Outers, Inners, and Lasts)
FOIL can help us greatly in this scenario. Let's start by multiplying the 'Firsts' together: 4x * 4x = <em>16x^2</em>
Now, lets to the 'Outers': 4x * -5y = <em>-20xy</em>
Next, we can multiply the 'Inners': -5y * 4x = <em>-20xy</em>
Finally, let's do the 'Lasts': -5y * -5y = <em>25y</em>^2
Now, we can take the products of these equations from FOIL and combine like terms. We have: 16x^2, -20xy, -20xy, and 25y^2. -20xy and -20xy make -40xy.
The final equation (product of (4x-5y)^2) is: 16x^2 - 40xy + 25y^2
Hope I helped! If any of my math is wrong, please report and let me know! Have a good one.