Question 259593
{{{(2b-1)^3=(2b-1)(2b-1)(2b-1)}}}
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 : {{{(highlight(2b)-1)(highlight(2b)-1)=(2b)(2b)=4b^2}}}
Outer : {{{(highlight(2b)-1)(2b+highlight(-1))=(2b)(-1)=-2b}}}
Inner : {{{(2b+highlight(-1))(highlight(2b)-1)=(-1)(2b)=-2b}}}
Last : {{{(2b+highlight(-1))(2b+highlight(-1))=(-1)(-1)=1}}}
{{{(2b-1)(2b-1)=4b^2-2b-2b+1}}}
{{{(2b-1)(2b-1)=4b^2-4b+1}}}
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{{{(2b-1)^3=(2b-1)(2b-1)(2b-1)}}}
{{{(2b-1)^3=(2b-1)(4b^2-4b+1)}}}
You can also use the distributive property like this,
{{{(2b-1)^3=(2b-1)(Z)}}}
{{{(2b-1)^3=2bZ-Z}}}
where {{{Z=4b^2-4b+1}}}, now that you've distributed Z you can go back and substitute for its real value.
{{{(2b-1)^3=2bZ-Z}}}
{{{(2b-1)^3=2b(4b^2-4b+1)-(4b^2-4b+1)}}}
{{{(2b-1)^3=(8b^3-8b^2+2b)-(4b^2-4b+1)}}}
{{{(2b-1)^3=8b^3-12b^2+6b-1}}}
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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.