document.write( "Question 1199431: It is possible to factor x^2 - y^2 by the technique of adding in an extra term, and taking it out again:\r
\n" ); document.write( "\n" ); document.write( "x^2 - y^2 = x^2 - xy + xy - y^2
\n" ); document.write( " = x(x - y) + y(x - y)
\n" ); document.write( " = (x + y)(x - y)\r
\n" ); document.write( "\n" ); document.write( "Apply this technique to determine a factorization of x^4 - y^4 \n" ); document.write( "

Algebra.Com's Answer #833310 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "Factoring  x^2 - y^2 = (x+y)*(x-y)  is the standard shortcut, known to all school students of adequate age/grade,\r\n" );
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document.write( "who learn/study Algebra.\r\n" );
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document.write( "So apply this shortcut twice to get\r\n" );
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document.write( "    x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 + y^2)*(x^2 - y^2) = factor (x^2-y^2) again = (x^2 + y^2)*(x+y)*(x-y).\r\n" );
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