document.write( "Question 443201: simplify (4x^4-9y^4)/(4x^4+12x^2y^2+9y^4) \n" ); document.write( "
Algebra.Com's Answer #305727 by swincher4391(1107)\"\" \"About 
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Notice that 4x^4 and 9y^4 are perfect squares.\r
\n" ); document.write( "\n" ); document.write( "(2x^2)^2 = 4x^4
\n" ); document.write( "(3y^2)^2 = 9y^4\r
\n" ); document.write( "\n" ); document.write( "We have the difference of squares:\r
\n" ); document.write( "\n" ); document.write( "Then, \"%284x%5E4+-+9y%5E4%29+=+%282x%5E2+%2B+3y%5E2%29%282x%5E2-3y%5E2%29\"\r
\n" ); document.write( "\n" ); document.write( "Noticing the same fact that 4x^4 and 9y^4 are perfect squares, and that (2*3)*2 = 12, we can say that \"%284x%5E4+%2B+12x%5E2y%5E2+%2B9y%5E4%29+=+%282x%5E2%2B3y%5E2%29%5E2\"\r
\n" ); document.write( "\n" ); document.write( "So we have \"%28%282x%5E2+%2B+3y%5E2%29%282x%5E2-3y%5E2%29%29%2F%282x%5E2%2B3y%5E2%29%5E2\"\r
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\n" ); document.write( "\"%282x%5E2-3y%5E2%29%2F%282x%5E2%2B3y%5E2%29\"\r
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