document.write( "Question 88986This question is from textbook algebra and trigonometry
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Algebra.Com's Answer #64695 by Edwin McCravy(20063) $\"\"$ $\"About$

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document.write( "Please help me with learning how to factor this polynomial. \r\n" );
document.write( "8a³ - 27\r\n" );
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document.write( "This is the difference of two cubes.\r\n" );
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document.write( "Notice that \r\n" );
document.write( "8 is the cube of 2\r\n" );
document.write( "x³ is the cube of x\r\n" );
document.write( "27 is the cube of 3\r\n" );
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document.write( "So the cube root of 8a³ is 2a and\r\n" );
document.write( "the cube root of 27 is 3.\r\n" );
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document.write( "The difference (respectively, sum) of two cubes is \r\n" );
document.write( "divisible by the difference (respectively, sum) of\r\n" );
document.write( "their cube roots.  \r\n" );
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document.write( "There are two methods:\r\n" );
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document.write( "Method 1:\r\n" );
document.write( "Use long division:\r\n" );
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document.write( "Divide 8a³ - 27 by the difference of the cube roots\r\n" );
document.write( "2a - 3.\r\n" );
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document.write( "First we have to insert placeholders since \r\n" );
document.write( "there is no a² or a terms. So we write 8a³ - 27\r\n" );
document.write( "as 8a³ + 0a² + 0a - 27\r\n" );
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document.write( "      ________4a²_+__6a +__9\r\n" );
document.write( "2a - 3)8a³ +  0a² +  0a - 27\r\n" );
document.write( "       8a³ - 12a²_  \r\n" );
document.write( "       ¯¯¯¯¯¯12a² +  0a\r\n" );
document.write( "             12a² - 18a_\r\n" );
document.write( "             ¯¯¯¯¯¯¯18a - 27\r\n" );
document.write( "                    18a - 27\r\n" );
document.write( "                    ¯¯¯¯¯¯¯¯\r\n" );
document.write( "                           0\r\n" );
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document.write( "So you see it factors as (2a - 3)(4a² + 6a + 9)\r\n" );
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document.write( "Method 2:\r\n" );
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document.write( "Memorize the following two rules, the first for the \r\n" );
document.write( "SUM of two cubes and the second for the DIFFERENCE of \r\n" );
document.write( "two cubes:\r\n" );
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document.write( " = \r\n" );
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document.write( " = \r\n" );
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document.write( "where FIRST represents the cube root of the first term, and\r\n" );
document.write( "SECOND represents the cube root of the second term.\r\n" );
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document.write( "Memorizing these will save you from having to use long division.\r\n" );
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document.write( "In this case, FIRST = cube root of 8a³ which is 2a and\r\n" );
document.write( "SECOND = cube root of 27, which is 3, so we use the rule for\r\n" );
document.write( "the DIFFERENCE of two cubes:\r\n" );
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document.write( " = \r\n" );
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document.write( "becomes: (2a - 3)(4a² + 6a + 9)\r\n" );
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document.write( "So if you don't like long division, then memorize the two\r\n" );
document.write( "rules and use method 2.\r\n" );
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document.write( "Edwin

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