document.write( "Question 586632: Can you please help me with this simplification problem? I can't figure out how to get it started and I can't find any examples in my book that are similar to it. \r
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Algebra.Com's Answer #373836 by eschwartz(9) $\"\"$ $\"About$

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: $\"%287e%5E%28-4x%29%29%2A2e%5E%282x%29\"$ simplifies to $\"14%2Ae%5E%28-2%2Ax%29\"$
Text form: (7e^(-4x))*2e^(2x) simplifies to 14*e^(-2*x)
Cartoon (animation) form: $\"simplify_cartoon%28+%287e%5E%28-4x%29%29%2A2e%5E%282x%29+%29\"$
For tutors: simplify_cartoon( (7e^(-4x))*2e^(2x) )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"highlight_red%28+%28highlight_red%28+7%2Ae%5E%28-4%2Ax%29+%29%29%2A2%2Ae%5E%282%2Ax%29+%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$ , $\"highlight_red%28+e%5E%28-4%2Ax%29+%29\"$
It becomes $\"highlight_green%28+7+%29%2Ahighlight_green%28+e%5E%28-4%2Ax%29+%29%2A2%2Ae%5E%282%2Ax%29\"$ .
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Look at $\"highlight_red%28+7+%29%2Ae%5E%28-4%2Ax%29%2Ahighlight_red%28+2+%29%2Ae%5E%282%2Ax%29\"$ .
Multiplied numerator integers
It becomes $\"highlight_green%28+14+%29%2Ae%5E%28-4%2Ax%29%2Ae%5E%282%2Ax%29\"$ .
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Look at $\"14%2Ahighlight_red%28+e%5E%28-4%2Ax%29+%29%2Ahighlight_red%28+e%5E%282%2Ax%29+%29\"$ .
Reduce similar several occurrences of $\"highlight_red%28+e%5E%28-4%2Ax%29+%29\"$ to $\"highlight_green%28+e%5E%28%28-4%2Ax%29%2B%282%2Ax%29%29+%29\"$
It becomes $\"14%2Ahighlight_green%28+e%5E%28%28-4%2Ax%29%2B%282%2Ax%29%29+%29\"$ .
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Look at $\"14%2Ae%5E%28highlight_red%28+%28-4%2Ax%29+%29%2B%282%2Ax%29%29\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+-4%2Ax+%29\"$
It becomes $\"14%2Ae%5E%28-highlight_green%28+4%2Ax+%29%2B%282%2Ax%29%29\"$ .
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Look at $\"14%2Ae%5E%28-4%2Ax%2Bhighlight_red%28+%282%2Ax%29+%29%29\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+2%2Ax+%29\"$
It becomes $\"14%2Ae%5E%28-4%2Ax%2Bhighlight_green%28+2%2Ax+%29%29\"$ .
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Look at $\"14%2Ae%5E%28-highlight_red%28+4%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29%29\"$ .
Eliminated similar terms $\"highlight_red%28+-4%2Ax+%29\"$ , $\"highlight_red%28+2%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-4%2B2%29%2Ax+%29\"$
It becomes $\"14%2Ae%5E%28highlight_green%28+%28-4%2B2%29%2Ax+%29%29\"$ .
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Look at $\"14%2Ae%5E%28%28-highlight_red%28+4+%29%2Bhighlight_red%28+2+%29%29%2Ax%29\"$ .
Added fractions or integers together
It becomes $\"14%2Ae%5E%28%28highlight_green%28+-2+%29%29%2Ax%29\"$ .
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Look at $\"14%2Ae%5E%28%28highlight_red%28+-2+%29%29%2Ax%29\"$ .
Removed extra sign in front of $\"-2\"$
It becomes $\"14%2Ae%5E%28%28-highlight_green%28+2+%29%29%2Ax%29\"$ .
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Look at $\"14%2Ae%5E%28highlight_red%28+%28-highlight_red%28+2+%29%29%2Ax+%29%29\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"14%2Ae%5E%28-highlight_green%28+2+%29%2Ax%29\"$ .
Result: $\"14%2Ae%5E%28-2%2Ax%29\"$
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Universal Simplifier and Solver

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Done!

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