Question 259593
this equation is the same as (2b-1) * (2b-1) * (2b-1)


first multiply (2b-1) * (2b-1) to get:


4b^2 - 2b - 2b + 1


combine like terms to get:


4b^2 - 4b + 1


then multiply (4b^2 - 4b + 1) * (2b-1) to get:


8b^3 - 4b^2 - 8b^2 + 4b + 2b - 1


combine like terms to get:


8b^3 - 12b^2 + 6b - 1


when you multiply polynomials together, you multiply every term in one polynomial by every term in the other polynomial.


(2b-1) * (2b-1) is multiplied together as follows:


2b from the left term is multiplied by 2b from the right term to get 4b^2
2b from the left term is multiplied by -1 from the right term to get -2b
-1 from the left term is multiplied by 2b from the right term to get -2b
-1 from the left term is multiplied by -1 from the right term to get +1


add all the terms together to get 4b^2 - 2b - 2b + 1
combine like terms to get 4b^2 - 4b + 1


(4b^2 - 4b + 1) * (2b-1) is multiplied together as follows:


4b^2 from the left term is multiplied by 2b from the right term to get 8b^3
4b^2 from the left term is multiplied by -1 from the right term to get -4b^2
-4b from the left term is multiplied by 2b from the right term to get -8b^2
-4b from the left term is multiplied by -1 from the right term to get 4b
1 from the left term is multiplied by 2b from the right term to get 2b
1 from the left term is multiplied by -1 from the right term to get -1


add all the terms together to get 8b^3 - 4b^2 - 8b^2 + 4b + 2b - 1
combine like terms to get 8b^3 - 12b^2 + 6b - 1