document.write( "Question 21366: Expand (x-2)(x-5)(x+7) \n" ); document.write( "

Algebra.Com's Answer #13578 by Alwayscheerful(414) $\"\"$ $\"About$

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: $\"%28x-2%29%2A%28x-5%29%2A%28x%2B7%29\"$ simplifies to $\"x%5E%283%29-39%2Ax%2B70\"$
Text form: (x-2)*(x-5)*(x+7) simplifies to x^(3)-39*x+70
Cartoon (animation) form: $\"simplify_cartoon%28+%28x-2%29%2A%28x-5%29%2A%28x%2B7%29+%29\"$
For tutors: simplify_cartoon( (x-2)*(x-5)*(x+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 $\"highlight_red%28+%28x-2%29%2A%28x-5%29%2A%28x%2B7%29+%29\"$ .
Expanded term $\"%28x-5%29%2A%28x%2B7%29\"$ by using associative property on $\"%28x-2%29\"$
It becomes

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Look at $\"highlight_red%28+%28x-5%29%2A%28x%2B7%29%2Ax+%29-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
Expanded term $\"%28x%2B7%29%2Ax\"$ by using associative property on $\"%28x-5%29\"$
It becomes

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Look at

.
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"%28x%2B7%29%2Ahighlight_green%28+x%5E2+%29-%28x%2B7%29%2Ax%2A5-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at $\"highlight_red%28+%28x%2B7%29%2Ax%5E2+%29-%28x%2B7%29%2Ax%2A5-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
Expanded term $\"x%5E2\"$ by using associative property on $\"%28x%2B7%29\"$
It becomes

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Look at

.
Reduce similar several occurrences of $\"highlight_red%28+x%5E2+%29\"$ to $\"highlight_green%28+x%5E%281%2B2%29+%29\"$
It becomes

.
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Look at

.
Added fractions or integers together
It becomes

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Look at $\"x%5E%283%29%2Bx%5E2%2A7-highlight_red%28+%28x%2B7%29%2Ax%2A5+%29-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
Expanded term $\"-x%2A5\"$ by using associative property on $\"%28x%2B7%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"x%5E%283%29%2Bx%5E2%2A7-x%2A5%2Ax-x%2Ahighlight_green%28+35+%29-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at

.
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"x%5E%283%29%2Bx%5E2%2A7-highlight_green%28+x%5E2+%29%2A5-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+x%5E2%2A7+%29\"$ , $\"highlight_red%28+-x%5E2%2A5+%29\"$ replacing them with $\"highlight_green%28+%287-5%29%2Ax%5E2+%29\"$
It becomes $\"x%5E%283%29%2Bhighlight_green%28+%287-5%29%2Ax%5E2+%29-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"x%5E%283%29%2B%28highlight_green%28+2+%29%29%2Ax%5E2-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at

.
Remove unneeded parentheses around factor $\"highlight_red%28+2+%29\"$
It becomes $\"x%5E%283%29%2Bhighlight_green%28+2+%29%2Ax%5E2-x%2A35-%28x-5%29%2A%28x%2B7%29%2A2\"$ .
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Look at $\"x%5E%283%29%2B2%2Ax%5E2-x%2A35-highlight_red%28+%28x-5%29%2A%28x%2B7%29%2A2+%29\"$ .
Expanded term $\"-%28x%2B7%29%2A2\"$ by using associative property on $\"%28x-5%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"x%5E%283%29%2B2%2Ax%5E2-x%2A35-%28x%2B7%29%2A2%2Ax%2B%28x%2B7%29%2Ahighlight_green%28+10+%29\"$ .
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Look at $\"x%5E%283%29%2B2%2Ax%5E2-x%2A35-highlight_red%28+%28x%2B7%29%2A2%2Ax+%29%2B%28x%2B7%29%2A10\"$ .
Expanded term $\"-2%2Ax\"$ by using associative property on $\"%28x%2B7%29\"$
It becomes

.
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Look at

.
Multiplied numerator integers
It becomes $\"x%5E%283%29%2B2%2Ax%5E2-x%2A35-2%2Ax%2Ax-highlight_green%28+14+%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at

.
Reduce similar several occurrences of $\"highlight_red%28+x+%29\"$ to $\"highlight_green%28+x%5E2+%29\"$
It becomes $\"x%5E%283%29%2B2%2Ax%5E2-x%2A35-2%2Ahighlight_green%28+x%5E2+%29-14%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+2%2Ax%5E2+%29\"$ , $\"highlight_red%28+-2%2Ax%5E2+%29\"$ replacing them with $\"highlight_green%28+%282-2%29%2Ax%5E2+%29\"$
It becomes $\"x%5E%283%29%2Bhighlight_green%28+%282-2%29%2Ax%5E2+%29-x%2A35-14%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at

.
Eliminated similar terms $\"highlight_red%28+-x%2A35+%29\"$ , $\"highlight_red%28+-14%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-35-14%29%2Ax+%29\"$
It becomes $\"x%5E%283%29%2B%282-2%29%2Ax%5E2%2Bhighlight_green%28+%28-35-14%29%2Ax+%29%2B%28x%2B7%29%2A10\"$ .
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Look at $\"x%5E%283%29%2Bhighlight_red%28+%282-2%29%2Ax%5E2+%29%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10\"$ .
Since $\"highlight_red%28+%282-2%29%2Ax%5E2+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"x%5E%283%29%2B0%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10\"$ .
Added fractions or integers together
It becomes $\"x%5E%283%29%2B0%2B%28-35-14%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"x%5E%283%29%2B0%2B%28highlight_green%28+-49+%29%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at $\"x%5E%283%29%2Bhighlight_red%28+0+%29%2B%28-49%29%2Ax%2B%28x%2B7%29%2A10\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"x%5E%283%29%2B%28-49%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at $\"x%5E%283%29%2B%28highlight_red%28+-49+%29%29%2Ax%2B%28x%2B7%29%2A10\"$ .
Removed extra sign in front of $\"-49\"$
It becomes $\"x%5E%283%29%2B%28-highlight_green%28+49+%29%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at $\"x%5E%283%29%2Bhighlight_red%28+%28-highlight_red%28+49+%29%29%2Ax+%29%2B%28x%2B7%29%2A10\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+49+%29\"$
It becomes $\"x%5E%283%29-highlight_green%28+49+%29%2Ax%2B%28x%2B7%29%2A10\"$ .
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Look at $\"x%5E%283%29-49%2Ax%2Bhighlight_red%28+%28x%2B7%29%2A10+%29\"$ .
Expanded term $\"10\"$ by using associative property on $\"%28x%2B7%29\"$
It becomes $\"x%5E%283%29-49%2Ax%2Bhighlight_green%28+10%2Ax+%29%2Bhighlight_green%28+10%2A7+%29\"$ .
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Look at $\"x%5E%283%29-49%2Ax%2B10%2Ax%2Bhighlight_red%28+10+%29%2Ahighlight_red%28+7+%29\"$ .
Multiplied numerator integers
It becomes $\"x%5E%283%29-49%2Ax%2B10%2Ax%2Bhighlight_green%28+70+%29\"$ .
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Look at $\"x%5E%283%29-highlight_red%28+49%2Ax+%29%2Bhighlight_red%28+10%2Ax+%29%2B70\"$ .
Eliminated similar terms $\"highlight_red%28+-49%2Ax+%29\"$ , $\"highlight_red%28+10%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28-49%2B10%29%2Ax+%29\"$
It becomes $\"x%5E%283%29%2Bhighlight_green%28+%28-49%2B10%29%2Ax+%29%2B70\"$ .
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Look at $\"x%5E%283%29%2B%28-highlight_red%28+49+%29%2Bhighlight_red%28+10+%29%29%2Ax%2B70\"$ .
Added fractions or integers together
It becomes $\"x%5E%283%29%2B%28highlight_green%28+-39+%29%29%2Ax%2B70\"$ .
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Look at $\"x%5E%283%29%2B%28highlight_red%28+-39+%29%29%2Ax%2B70\"$ .
Removed extra sign in front of $\"-39\"$
It becomes $\"x%5E%283%29%2B%28-highlight_green%28+39+%29%29%2Ax%2B70\"$ .
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Look at $\"x%5E%283%29%2Bhighlight_red%28+%28-highlight_red%28+39+%29%29%2Ax+%29%2B70\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+39+%29\"$
It becomes $\"x%5E%283%29-highlight_green%28+39+%29%2Ax%2B70\"$ .
Result: $\"x%5E%283%29-39%2Ax%2B70\"$
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Universal Simplifier and Solver

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Done!

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