document.write( "Question 166514: For x²(a-b)+a²(b-x)+b²(x-a) show that (x-a) is a linear factor.
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Algebra.Com's Answer #122719 by ptaylor(2198) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, get rid of parens
\n" ); document.write( " $\"x%5E2a-x%5E2b%2Ba%5E2b-a%5E2x%2Bb%5E2x-b%5E2a\"$ rearrange and regroup
\n" ); document.write( " $\"%28a-b%29x%5E2-%28a%5E2-b%5E2%29x%2B%28a%5E2b-b%5E2a%29\"$ expand $\"%28a%5E2-b%5E2%29\"$
\n" ); document.write( " $\"%28a-b%29x%5E2-%28a-b%29%28a%2Bb%29x%2Bab%28a-b%29\"$ factor out $\"%28a-b%29\"$
\n" ); document.write( " $\"%28a-b%29%28x%5E2-%28a-b%29x%2Bab%29\"$ =
\n" ); document.write( "Since $\"x%5E2-%28a-b%29x%2Bab\"$ equals $\"%28x-a%29%28x-b%29\"$ , we have\r
\n" ); document.write( "\n" ); document.write( " $\"%28a-b%29%28x-a%29%28x-b%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Hope this helps---ptaylor
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