SOLUTION: Alright the question is (2b-1)^3 I got: 8b-1 but the answer is: 8b^3-12b^2+6b-1 How does that work? P.S ^3 and ^2 mean to the third power and second power.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Alright the question is (2b-1)^3 I got: 8b-1 but the answer is: 8b^3-12b^2+6b-1 How does that work? P.S ^3 and ^2 mean to the third power and second power.      Log On


   

Question 259593: Alright the question is (2b-1)^3
I got: 8b-1
but the answer is:
8b^3-12b^2+6b-1
How does that work?
P.S ^3 and ^2 mean to the third power and second power.
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%282b-1%29%5E3=%282b-1%29%282b-1%29%282b-1%29
Let's break it down to smaller problem first using the FOIL Method.
FOIL Method (First Outer Inner Last)to find the product of (2b-1)(2b-1)
First : %28highlight%282b%29-1%29%28highlight%282b%29-1%29=%282b%29%282b%29=4b%5E2
Outer : %28highlight%282b%29-1%29%282b%2Bhighlight%28-1%29%29=%282b%29%28-1%29=-2b
Inner : %282b%2Bhighlight%28-1%29%29%28highlight%282b%29-1%29=%28-1%29%282b%29=-2b
Last : %282b%2Bhighlight%28-1%29%29%282b%2Bhighlight%28-1%29%29=%28-1%29%28-1%29=1
%282b-1%29%282b-1%29=4b%5E2-2b-2b%2B1
%282b-1%29%282b-1%29=4b%5E2-4b%2B1
.
.
.
%282b-1%29%5E3=%282b-1%29%282b-1%29%282b-1%29
%282b-1%29%5E3=%282b-1%29%284b%5E2-4b%2B1%29
You can also use the distributive property like this,
%282b-1%29%5E3=%282b-1%29%28Z%29
%282b-1%29%5E3=2bZ-Z
where Z=4b%5E2-4b%2B1, now that you've distributed Z you can go back and substitute for its real value.
%282b-1%29%5E3=2bZ-Z
%282b-1%29%5E3=2b%284b%5E2-4b%2B1%29-%284b%5E2-4b%2B1%29
%282b-1%29%5E3=%288b%5E3-8b%5E2%2B2b%29-%284b%5E2-4b%2B1%29
%282b-1%29%5E3=8b%5E3-12b%5E2%2B6b-1
.
.
.
The FOIL Method is really the same distributive property we used in the second part. It's just done to help you remember to properly distribute all of the terms.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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