document.write( "Question 62896: need help
\n" ); document.write( "Reduce (64y^3+27z^3)/(4y+3y) to lowest terms\r
\n" ); document.write( "\n" ); document.write( "choices are 16y^2+12yz-9z^2
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\n" ); document.write( " 16y^2-12yz+9z^2
\n" ); document.write( " already in lowest terms \n" ); document.write( "
Algebra.Com's Answer #43718 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Reduce (64y^3+27z^3)/(4y+3y) \r\n" );
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document.write( " (4y)² + (3z)²\r\n" );
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document.write( "    4y + 3z \r\n" );
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document.write( "to lowest terms choices are\r\n" );
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document.write( "16y² + 12yz - 9z²\r\n" );
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document.write( "4y + 3z\r\n" );
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document.write( "16y² - 12yz + 9z²\r\n" );
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document.write( "already in lowest terms\r\n" );
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document.write( "-----------------------------------------\r\n" );
document.write( "Notice that I have placed parentheses around\r\n" );
document.write( "both the numerator and the denominator as must\r\n" );
document.write( "be done when typing an algebraic fraction all\r\n" );
document.write( "on one line whenever there is more than just \r\n" );
document.write( "one number or only one letter in the numerator \r\n" );
document.write( "or denominator.  You of course don't need\r\n" );
document.write( "parentheses when typing it on two separate\r\n" );
document.write( "lines like this:\r\n" );
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document.write( " 64y³ + 27z³\r\n" );
document.write( "-------------\r\n" );
document.write( "   4y + 3y \r\n" );
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document.write( "The numerator can be rewritten as\r\n" );
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document.write( " (4y)² + (3z)²\r\n" );
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document.write( "    4y + 3z \r\n" );
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document.write( "Factor the numerator, (4y)³ + (3z)³,\r\n" );
document.write( "using the principle:\r\n" );
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document.write( "A³ + B³ = (A + B)(A² - AB + B²)\r\n" );
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document.write( "where A = 4y and B = 3z, so we have\r\n" );
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document.write( "Let's isolate the numerator to work with it.\r\n" );
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document.write( "(4y)² + (3z)² = \r\n" );
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document.write( "(4y + 3z)[(4y)² - (4y)(3z) + (3z)²]\r\n" );
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document.write( "=  (4y + 3z)(16y² - 12yz + 9z²)\r\n" );
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document.write( "Now place it over the denominator\r\n" );
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document.write( "  (4y + 3z)(16y² - 12yz + 9z²)\r\n" );
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document.write( "            4y + 3z\r\n" );
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document.write( "Now we cancel the entire denominator into the\r\n" );
document.write( "first factor of the numerator:\r\n" );
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document.write( "      1\r\n" );
document.write( "  (4y + 3z)(16y² - 12yz + 9z²)\r\n" );
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document.write( "            4y + 3z\r\n" );
document.write( "               1\r\n" );
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document.write( "All that's left is\r\n" );
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document.write( "        16y² - 12yz + 9z²\r\n" );
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document.write( "which is the third choice.\r\n" );
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document.write( "Edwin
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