(a + 3b)^2 - (3a + b)^2

(a + 3b)² - (3a + b)²=a²+6ab+9b²-(9a²+6ab+b²)= a²+6ab+9b²-9a²-6ab-b²= 8b²-8a²=8(b²-a²)=8(b-a)(b+a)