Question 887044
<pre>
We will use 

1. {{{j^2=-1}}}, 
2. {{{(-1)^EVEN=1}}}, 
3. {{{(-1)^ODD=-1}}}, 
4. {{{j^ODD=J^EVEN*j}}}, 
5. {{{j^EVEN=(j^2)^N}}}

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{{{8j^23 - 8(j^3)^2}}}

          We multiply exponents

{{{8j^23 - 8j^6}}}

          We factor out 8

{{{8(j^23-j^6)}}}

          Break odd power of j into even power times j:
          Write even power as power of jē:

{{{8(j^22*j-(j^2)^3)}}}

          Write even power as power of jē
          Substitute -1 for jē:

{{{8((j^2)^11*j-(-1)^3)}}}

          Substitute -1 for jē:
          Use {{{(-1)^ODD=-1}}}

{{{8((-1)^11*j-(-1))}}}

          Use {{{(-1)^ODD=-1}}}
          Write -(-1) as +1

{{{8((-1)*j+1)}}}

          Write (-1)*j as -j

{{{8(-j+1)}}}

          Distribute 8

{{{-8j+8}}}

          Write j-term second:

{{{8-8j}}}

Edwin</pre>