Hi there!
You can use distributive property to solve this equation.
These are the list of terms you have to multiply :
a × a² = a³
a × -ab = -a²b
a × b² = ab²
b × a² = a²b
b × -ab = -ab²
b × b² = b³
add all of those terms...
a³ - a²b + ab² +a²b -ab² + b³
simplify by adding like terms... (- a²b + a²b , ab² - ab²)
a³ + b³
Hope this helped!! :)