(4x+5y)^2-(4x-5y)^2 how do I factor this?

Question

(4x+5y)^2-(4x-5y)^2 how do I factor this? I do not know what to do after the problem is in the difference of squares formula: [(4x+5y)+(4x-5y)][(4x+5y)-(4x-5y)] 

Answer 1

Just multiply it out:

 

(4x+5y)² - (4x-5y)²

 

= 16x² + 40xy + 25y² - (16x² - 40xy + 25y²)

 

= 80xy

 

You can also solve it using the difference of squares formula:

 

a² - b² = (a-b)(a+b)

 

Where a=4x+5y and b=4x-5y

 

(4x+5y-4x+5y)(4x+5y+4x-5y)

 

(10y)(8x) = 80xy