document.write( "Question 789866: if a^2+b^2=c^2 than prove that (a+b+c)(b+c-a)(c+a-b)(a+b-c)=4a^2b^2 \n" ); document.write( "
Algebra.Com's Answer #478997 by Edwin McCravy(20064)\"\" \"About 
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document.write( "           (a+b+c)(b+c-a)(c+a-b)(a+b-c) ≟ 4a²b²\r\n" );
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document.write( "Write the last factor second:\r\n" );
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document.write( "           (a+b+c)(a+b-c)(b+c-a)(c+a-b) ≟ 4a²b²\r\n" );
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document.write( "Rearrange and regroup each factor:\r\n" );
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document.write( "(a+b+c) = [b+c+a] = [(b+c)+a]\r\n" );
document.write( "(a+b-c) = [a-c+b] = [a+b-c] = [a+(b-c)]\r\n" );
document.write( "(b+c-a) = [b+c-a] = [(b+c)-a] \r\n" );
document.write( "(c+a-b) = [a-b+c] = [a-(b-c)]\r\n" );
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document.write( "           (a+b+c)(a+b-c)(b+c-a)(c+a-b) ≟ 4a²b²\r\n" );
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document.write( "      [(a+b)+c][(a+b)-c][b-a+c][-b+a+c] ≟ 4a²b²\r\n" );
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document.write( "  [(a+b)+c][(a+b)-c][(b-a)+c][-(b-a)+c] ≟ 4a²b²\r\n" );
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document.write( "                [(a+b)²-c²][-(b-a)²+c²] ≟ 4a²b²\r\n" );
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document.write( "      [(a²+2ab+b²)-c²][-(b²-2ba+a²)+c²] ≟ 4a²b²\r\n" );
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document.write( "          [a²+2ab+b²-c²][-b²+2ba-a²+c²] ≟ 4a²b²\r\n" );
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document.write( "Substitute a²+b² for c²\r\n" );
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document.write( "[a²+2ab+b²-(a²+b²)][-b²+2ba-a²+(a²+b²)] ≟ 4a²b²\r\n" );
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document.write( "    [a²+2ab+b²-a²-b²][-b²+2ba-a²+a²+b²] ≟ 4a²b²\r\n" );
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document.write( "           [b²+2bc+c²-a²][a²-b²+2bc-c²] ≟ 4a²b²\r\n" );
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document.write( "Substitute a²+b² for each c²\r\n" );
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document.write( " [b²+2bc+(a²+b²)-a²][a²-b²+2bc-(a²+b²)] ≟ 4a²b²\r\n" );
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document.write( "     [b²+2bc+a²+b²-a²][a²-b²+2bc-a²-b²] ≟ 4a²b²\r\n" );
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document.write( "                             [2ab][2ba] ≟ 4a²b²\r\n" );
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document.write( "                                  4a²b² ≡ 4a²b²\r\n" );
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document.write( "Edwin
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