(a+6b)cube ?

(a + 6b)^3
= (a + 6b)(a + 6b)^2
= (a + 6b)(a^2 + 12ab + 36b^2)
= a^3 + 12a^2b + 36ab^2 + 6a^2b + 72ab^2 + 216b^3
= a^3 + 18a^2b + 108ab^2 + 216b^3

(a + 6b)^3
= (a + 6b)(a + 6b)(a + 6b)
= (a*a + 6b*a + a*6b + 6b*6b)(a + 6b)
= (a^2 + 6ab + 6ab + 36b^2)(a + 6b)
= (a^2 + 12ab + 36b^2)(a + 6b)
= a^2*a + 12ab*a + 36b^2*a + a^2*6b + 12ab*6b + 36b^2*6b
= a^3 + 12a^2b + 36ab^2 + 6a^2b + 72ab^2 + 216b^3
= a^3 + 12a^2b + 6a^2b + 36ab^2 + 72ab^2 + 216b^3
= a^3 + 18a^2b + 108ab^2 + 216b^3

(a + 6b)(a² + 12ab + 36b²)

a³ + 12a²b + 36ab²
_____6a²b + 72ab² + 216b³

a³ + 18a²b + 108ab² + 216b³

(a + 6b)^3 ==>

This means that you have to MULTIPLY the term 3 times by itself.

(a + 6b)^3 = (a+6b) (a+6b)(a+6b)

Multiply first the 1st and the 2nd term

(a+6b) ( a+6b) = a^2 + 6ab + 6ab + 36b^2

Combine like terms

a^2 + 12ab + 36b^2

Multiply this by the 3rd term

(a^2 + 12ab + 36b^2) ( a + 6b) =

a^3 + 12a^2b + 36ab^2 + 6a^2b + 72ab^2 + 216b^3

Combine like terms

a^3 + 18a^2b + 108ab^2 + 216b^3 ==> the answer

a^3+((3C1)(a)^2 x(6b))+((3C2)(a) x(6b)^2)+(6b)^3\

c=NCR

Just do your hw...