Factor: x^2+8xy+15y^2

We look for a pair of terms that multiply to 15y^2 and add properly to 8y and we discover 3y and 5y will work: 
X^2+8xy+15y^2=
X^2+x(3y+5y)+15y^2=
X^2+3xy +5xy+15y^2=
(X^2+3xy)+(5xy+15y^2)=
x(x+3y)+5y(x+3y)=
(x+5y)(x+3y) 

:)