document.write( "Question 548460: Factor out the greatest common factor from the following expression: 24xyz^2 + 20x^2yz - 4x^2z^2. \n" ); document.write( "
Algebra.Com's Answer #357045 by Edwin McCravy(20056)\"\" \"About 
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document.write( "24xyz² + 20x²yz - 4x²z²\r\n" );
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document.write( "1.  We look for the largest number we can factor out of all three terms:\r\n" );
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document.write( "24, 20 and 4 can all be divided evenly by 4, so we can take out a 4\r\n" );
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document.write( "2.  Now we look for the largest power of a letter we can factor out of\r\n" );
document.write( "all three terms:\r\n" );
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document.write( "x occurs in all three terms. The smallest power of x is x1. So we can factor out x\r\n" );
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document.write( "y does not occur in all three terms, so we cannot take out y\r\n" );
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document.write( "z occurs in all three terms. The smallest power of z is z1. So we can factor out z.\r\n" );
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document.write( "3.  So the GCF is their product 4xz\r\n" );
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document.write( "4.  Start with this\r\n" );
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document.write( "4xz(\r\n" );
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document.write( "In order to get the first term 24xyz², if we were to use the \r\n" );
document.write( "distributive principle, the 4xz would need to be multiplied by a \"6\", a \"y\",\r\n" );
document.write( "and a \"z\". So we write\r\n" );
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document.write( "4xz(6yz\r\n" );
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document.write( "In order to get the second term +20x²yz the 4xz will need to be multiplied\r\n" );
document.write( "by a \"+5\", an \"x\", and a y. So we write\r\n" );
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document.write( "4xz(6yz + 5xy\r\n" );
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document.write( "In order to get the third term - 4x²z² the 4xz will need to be multiplied \r\n" );
document.write( "by a \"-x\", and a z. So we write\r\n" );
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document.write( "4xz(6yz + 5xy - xz\r\n" );
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document.write( "and close the parentheses:\r\n" );
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document.write( "4xz(6yz + 5xy - xz)\r\n" );
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document.write( "That's it.  Check by using the distributive principle to remove the\r\n" );
document.write( "parentheses and you will get what you started with.\r\n" );
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document.write( "Edwin
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