Answer
$ 4x^2-25y^2$.
Work Step by Step
Use the FOIL method.
$\Rightarrow (2x-5y)(2x+5y)=2x(2x+5y)-5y(2x+5y)$
First $\rightarrow 2x\cdot 2x=4x^2$
Outside $\rightarrow 2x\cdot 5y=10xy$
Inside $\rightarrow (-5y)\cdot 2x=-10xy$
Last $\rightarrow (-5y)\cdot (5y)=-25y^2$
The product is
$\Rightarrow 4x^2+10xy-10xy-25y^2$
Add like terms.
$\Rightarrow =4x^2-25y^2$.
Another solution:
Notice that we can use the special formula
$(A-B)(A+B)=A^2-B^2$,
where $A=2x$ and $B=5y$:
$(2x-5y)(2x+5y)=(2x)^2-(5y)^2$
$=4x^2-25y^2$
