Question

establish the formula by cut & paste method
(a+b)^3=a^3+3a^2b+3ab^2+b^3

Answer 1

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

Answer 2

(a+b)³ = (a+b)(a+b)(a+b)
         = a²+ab+ab+b²(a+b)
         = a²+2ab+b²(a+b)
         = a³+2a²b+2ab²+b³