document.write( "Question 6582: i need help with like-terms. here is one of my problems...... \r
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Algebra.Com's Answer #3582 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: $\"%286v%5E5-5v%29-5%2A%287v%5E5-2v-7%29\"$ simplifies to $\"-29%2Av%5E5%2B5%2Av%2B35\"$
Text form: (6v^5-5v)-5*(7v^5-2v-7) simplifies to -29*v^5+5*v+35
Cartoon (animation) form: $\"simplify_cartoon%28+%286v%5E5-5v%29-5%2A%287v%5E5-2v-7%29+%29\"$
For tutors: simplify_cartoon( (6v^5-5v)-5*(7v^5-2v-7) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+%286%2Av%5E5-5%2Av%29+%29-5%2A%287%2Av%5E5-2%2Av-7%29\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+6%2Av%5E5+%29\"$ , $\"highlight_red%28+-5%2Av+%29\"$
It becomes $\"highlight_green%28+6%2Av%5E5+%29-highlight_green%28+5%2Av+%29-5%2A%287%2Av%5E5-2%2Av-7%29\"$ .
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Look at $\"6%2Av%5E5-5%2Av-highlight_red%28+5%2A%287%2Av%5E5-2%2Av-7%29+%29\"$ .
Expanded term $\"-5\"$ by using associative property on $\"%287%2Av%5E5-2%2Av-7%29\"$
It becomes

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Look at $\"6%2Av%5E5-5%2Av-highlight_red%28+5+%29%2Ahighlight_red%28+7+%29%2Av%5E5%2B5%2A2%2Av%2B5%2A7\"$ .
Multiplied numerator integers
It becomes $\"6%2Av%5E5-5%2Av-highlight_green%28+35+%29%2Av%5E5%2B5%2A2%2Av%2B5%2A7\"$ .
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Look at $\"6%2Av%5E5-5%2Av-35%2Av%5E5%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+2+%29%2Av%2B5%2A7\"$ .
Multiplied numerator integers
It becomes $\"6%2Av%5E5-5%2Av-35%2Av%5E5%2Bhighlight_green%28+10+%29%2Av%2B5%2A7\"$ .
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Look at $\"6%2Av%5E5-5%2Av-35%2Av%5E5%2B10%2Av%2Bhighlight_red%28+5+%29%2Ahighlight_red%28+7+%29\"$ .
Multiplied numerator integers
It becomes $\"6%2Av%5E5-5%2Av-35%2Av%5E5%2B10%2Av%2Bhighlight_green%28+35+%29\"$ .
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Look at $\"highlight_red%28+6%2Av%5E5+%29-5%2Av-highlight_red%28+35%2Av%5E5+%29%2B10%2Av%2B35\"$ .
Eliminated similar terms $\"highlight_red%28+6%2Av%5E5+%29\"$ , $\"highlight_red%28+-35%2Av%5E5+%29\"$ replacing them with $\"highlight_green%28+%286-35%29%2Av%5E5+%29\"$
It becomes $\"highlight_green%28+%286-35%29%2Av%5E5+%29-5%2Av%2B10%2Av%2B35\"$ .
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Look at $\"%286-35%29%2Av%5E5-highlight_red%28+5%2Av+%29%2Bhighlight_red%28+10%2Av+%29%2B35\"$ .
Eliminated similar terms $\"highlight_red%28+-5%2Av+%29\"$ , $\"highlight_red%28+10%2Av+%29\"$ replacing them with $\"highlight_green%28+%28-5%2B10%29%2Av+%29\"$
It becomes $\"%286-35%29%2Av%5E5%2Bhighlight_green%28+%28-5%2B10%29%2Av+%29%2B35\"$ .
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Look at $\"%28highlight_red%28+6+%29-highlight_red%28+35+%29%29%2Av%5E5%2B%28-5%2B10%29%2Av%2B35\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+-29+%29%29%2Av%5E5%2B%28-5%2B10%29%2Av%2B35\"$ .
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Look at $\"%28-29%29%2Av%5E5%2B%28-highlight_red%28+5+%29%2Bhighlight_red%28+10+%29%29%2Av%2B35\"$ .
Added fractions or integers together
It becomes $\"%28-29%29%2Av%5E5%2B%28highlight_green%28+5+%29%29%2Av%2B35\"$ .
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Look at $\"%28highlight_red%28+-29+%29%29%2Av%5E5%2B%285%29%2Av%2B35\"$ .
Removed extra sign in front of $\"-29\"$
It becomes $\"%28-highlight_green%28+29+%29%29%2Av%5E5%2B%285%29%2Av%2B35\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+29+%29%29%2Av%5E5+%29%2B%285%29%2Av%2B35\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+29+%29\"$
It becomes $\"-highlight_green%28+29+%29%2Av%5E5%2B%285%29%2Av%2B35\"$ .
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Look at $\"-29%2Av%5E5%2Bhighlight_red%28+%28highlight_red%28+5+%29%29%2Av+%29%2B35\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+5+%29\"$
It becomes $\"-29%2Av%5E5%2Bhighlight_green%28+5+%29%2Av%2B35\"$ .
Result: $\"-29%2Av%5E5%2B5%2Av%2B35\"$
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Universal Simplifier and Solver

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Done!

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