document.write( "Question 6788: Dear Tutor,
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Algebra.Com's Answer #3738 by ichudov(507) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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Graphical form: $\"2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29\"$ simplifies to $\"-60%2Aa%2B26%2Ab-24%2Axb\"$
Text form: 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) simplifies to -60*a+26*b-24*xb
Cartoon (animation) form: $\"simplify_cartoon%28+2a-%284%2A%28b-3%2A%28a-2xb-2a%29%29-10%2A%283b-5a%29%29+%29\"$
For tutors: simplify_cartoon( 2a-(4*(b-3*(a-2xb-2a))-10*(3b-5a)) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2Aa-highlight_red%28+%284%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29-10%2A%283%2Ab-5%2Aa%29%29+%29\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+-4%2A%28b-3%2A%28a-2%2Axb-2%2Aa%29%29+%29\"$ , $\"highlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29\"$
It becomes

.
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Look at

.
Eliminated similar terms $\"highlight_red%28+a+%29\"$ , $\"highlight_red%28+-2%2Aa+%29\"$ replacing them with $\"highlight_green%28+%281-2%29%2Aa+%29\"$
It becomes

.
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Look at

.
Added fractions or integers together
It becomes

.
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Look at

.
Removed extra sign in front of $\"-1\"$
It becomes

.
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Look at

.
Remove unneeded parentheses around factor $\"highlight_red%28+1+%29\"$
It becomes $\"2%2Aa-4%2A%28b-3%2A%28-highlight_green%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at $\"2%2Aa-4%2A%28b-3%2A%28-highlight_red%28+1+%29%2Aa-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29\"$ .
Remove extraneous '1' from product $\"highlight_red%28+1+%29\"$
It becomes $\"2%2Aa-4%2A%28b-3%2A%28-a-2%2Axb%29%29%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at $\"2%2Aa-4%2A%28b-highlight_red%28+3%2A%28-a-2%2Axb%29+%29%29%2B10%2A%283%2Ab-5%2Aa%29\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28-a-2%2Axb%29\"$
It becomes

.
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Look at $\"2%2Aa-highlight_red%28+4%2A%28b%2B3%2Aa%2B3%2A2%2Axb%29+%29%2B10%2A%283%2Ab-5%2Aa%29\"$ .
Expanded term $\"-4\"$ by using associative property on $\"%28b%2B3%2Aa%2B3%2A2%2Axb%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"2%2Aa-4%2Ab-highlight_green%28+12+%29%2Aa-4%2A3%2A2%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at

.
Multiplied numerator integers
It becomes $\"2%2Aa-4%2Ab-12%2Aa-highlight_green%28+24+%29%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+2%2Aa+%29\"$ , $\"highlight_red%28+-12%2Aa+%29\"$ replacing them with $\"highlight_green%28+%282-12%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%282-12%29%2Aa+%29-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"%28highlight_green%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at $\"%28highlight_red%28+-10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
Removed extra sign in front of $\"-10\"$
It becomes $\"%28-highlight_green%28+10+%29%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at

.
Remove unneeded parentheses around factor $\"highlight_red%28+10+%29\"$
It becomes $\"-highlight_green%28+10+%29%2Aa-4%2Ab-24%2Axb%2B10%2A%283%2Ab-5%2Aa%29\"$ .
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Look at $\"-10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10%2A%283%2Ab-5%2Aa%29+%29\"$ .
Expanded term $\"10\"$ by using associative property on $\"%283%2Ab-5%2Aa%29\"$
It becomes $\"-10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+10%2A3%2Ab+%29-highlight_green%28+10%2A5%2Aa+%29\"$ .
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Look at $\"-10%2Aa-4%2Ab-24%2Axb%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+3+%29%2Ab-10%2A5%2Aa\"$ .
Multiplied numerator integers
It becomes $\"-10%2Aa-4%2Ab-24%2Axb%2Bhighlight_green%28+30+%29%2Ab-10%2A5%2Aa\"$ .
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Look at $\"-10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+10+%29%2Ahighlight_red%28+5+%29%2Aa\"$ .
Multiplied numerator integers
It becomes $\"-10%2Aa-4%2Ab-24%2Axb%2B30%2Ab-highlight_green%28+50+%29%2Aa\"$ .
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Look at $\"-highlight_red%28+10%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab-highlight_red%28+50%2Aa+%29\"$ .
Eliminated similar terms $\"highlight_red%28+-10%2Aa+%29\"$ , $\"highlight_red%28+-50%2Aa+%29\"$ replacing them with $\"highlight_green%28+%28-10-50%29%2Aa+%29\"$
It becomes $\"highlight_green%28+%28-10-50%29%2Aa+%29-4%2Ab-24%2Axb%2B30%2Ab\"$ .
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Look at $\"%28-10-50%29%2Aa-highlight_red%28+4%2Ab+%29-24%2Axb%2Bhighlight_red%28+30%2Ab+%29\"$ .
Eliminated similar terms $\"highlight_red%28+-4%2Ab+%29\"$ , $\"highlight_red%28+30%2Ab+%29\"$ replacing them with $\"highlight_green%28+%28-4%2B30%29%2Ab+%29\"$
It becomes $\"%28-10-50%29%2Aa%2Bhighlight_green%28+%28-4%2B30%29%2Ab+%29-24%2Axb\"$ .
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Look at $\"%28-highlight_red%28+10+%29-highlight_red%28+50+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-60+%29%29%2Aa%2B%28-4%2B30%29%2Ab-24%2Axb\"$ .
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Look at $\"%28-60%29%2Aa%2B%28-highlight_red%28+4+%29%2Bhighlight_red%28+30+%29%29%2Ab-24%2Axb\"$ .
Added fractions or integers together
It becomes $\"%28-60%29%2Aa%2B%28highlight_green%28+26+%29%29%2Ab-24%2Axb\"$ .
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Look at $\"%28highlight_red%28+-60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb\"$ .
Removed extra sign in front of $\"-60\"$
It becomes $\"%28-highlight_green%28+60+%29%29%2Aa%2B%2826%29%2Ab-24%2Axb\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+60+%29%29%2Aa+%29%2B%2826%29%2Ab-24%2Axb\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+60+%29\"$
It becomes $\"-highlight_green%28+60+%29%2Aa%2B%2826%29%2Ab-24%2Axb\"$ .
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Look at $\"-60%2Aa%2Bhighlight_red%28+%28highlight_red%28+26+%29%29%2Ab+%29-24%2Axb\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+26+%29\"$
It becomes $\"-60%2Aa%2Bhighlight_green%28+26+%29%2Ab-24%2Axb\"$ .
Result: $\"-60%2Aa%2B26%2Ab-24%2Axb\"$
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Universal Simplifier and Solver

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Done!

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