Question 101336
Factor:
{{{25x^2-81y^2}}} Do you see that this binomial is the difference of two squares?
{{{(5x)^2-(9y)^2}}}
The difference of two squares can be factored thus:
{{{A^2-B^2 = (A+B)(A-B)}}} Applying this to your problem, we get:
{{{25x^2-81y^2 = (5x)^2-(9y)^2}}} = {{{(5x+9y)(5x-9y)}}}
You can confirm this by using the FOIL method to multiply the resultant factors:
{{{(5x+9y)(5x-9y) = 25x^2cross(-45xy)+cross(45xy)-81y^2}}} The two middle terms drop out to leave you with:
{{{25x^2-81y^2}}}