Answer:
[tex](a+b)(a^2-ab+b^2)=a^3+b^3[/tex]
Step-by-step explanation:
Given expression:
[tex](a+b)(a^2-ab+b^2)[/tex]
Using the Distributive Property Law, expand the brackets:
[tex]\implies a(a^2-ab+b^2)+b(a^2-ab+b^2)[/tex]
[tex]\implies a^3-a^2b+ab^2+a^2b-ab^2+b^3[/tex]
Group like terms:
[tex]\implies a^3+b^3-a^2b+a^2b+ab^2-ab^2[/tex]
As -a²b+a²b=0 and ab²-ab²=0 then:
[tex]\implies a^3+b^3[/tex]
