Question

what is (a+b)^3 and (a+b)^4?

Answer 1

(a+b)^3
= (a+b)(a+b)(a+b)
= (a^2 + 2ab + b^2)(a+b)
= a^3 + (a^2)b + 2(a^2)b + 2a(b^2) +ab^2 +b^3
=a^3 +3(a^2)b + 3a(b^2) + b^3

for (a+b)^4 continue on by multiplying the first answer by another (a+b)
= (a^3 +3(a^2)b + 3a(b^2) + b^3)(a+b)
= a^4 +3(a^3)b + 3(a^2)(b^2) + ab^3 + (a^3)b +3(a^2)(b^2) + 3a(b^3) + b^4
...and then group terms...

Answer 2

a^3+b^3+3a^2b+3ab^2

Answer 3

so for (a+b)^4 the final answer is
= a^4 +4(a^3)b + 6(a^2)(b^2) + 4a(b^3) + b^4