what is the formula for (a+b)^3 ?

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

(a+b)^3 = (a+b)*(a+b)*(a+b)
= (a+b)*(a^2+b*a+a*b+b^2)
= (a+b)*(a^2+2*a*b+b^2)
= a^3+2*a^2*b+a*b^2+b*a^2+2*a*b^2+b^3
Combine like terms...

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

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

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

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

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


-rds

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

(a + b) ( a² + 2ab + b ² )

a ³ + 2a² b + ab²
_____a² b + 2ab² + b ³

a ³ + 3 a² b + 3ab² + b ³

That is Newton's expansion of the perfect cube:

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