document.write( "Question 1127762: states the first three terms in the expansionof (1+ax+bx^2)^4, if there are 1+8x+12x^2, find the values of a and b. \n" ); document.write( "
Algebra.Com's Answer #744411 by Edwin McCravy(20066)\"\" \"About 
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document.write( "The expansion is the sum of all possible products of four factors,\r\n" );
document.write( "each factor being one term from each of the four parentheses.\r\n" );
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document.write( "The first term is a constant, so it's the product of the\r\n" );
document.write( "four 1's, 1∙1∙1∙1 = 1, so\r\n" );
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document.write( "first term = 1\r\n" );
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document.write( "The second term is in x, so it's the sum of the products\r\n" );
document.write( "of three 1's and one ax.  So it's\r\n" );
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document.write( "1∙1∙1∙ax + 1∙1∙ax∙1 + 1∙ax∙1·1 + ax∙1∙1∙1 = ax + ax + ax + ax = 4ax, so\r\n" );
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document.write( "second term = 4ax\r\n" );
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document.write( "The third term is in x², so it's the sum of the products\r\n" );
document.write( "of two 1's and two ax's PLUS the sum of the products of\r\n" );
document.write( "three 1's and one bx².  So it's this:\r\n" );
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document.write( "1∙1∙ax∙ax + 1∙ax∙1∙ax + ax∙1·1∙ax + 1∙ax∙ax∙1 + ax∙1∙ax∙1 + ax∙ax∙1∙1 = 6a²x²\r\n" );
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document.write( "PLUS\r\n" );
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document.write( "1∙1∙1∙bx² + 1∙1∙bx²∙1 + 1∙bx²∙1 + bx²∙1∙1∙1 = bx² + bx² + bx² + bx² = 4bx²\r\n" );
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document.write( "third term = 6a²x² + 4bx² = (6a² + 4b)x² \r\n" );
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document.write( "We are given that the first three terms are 1 + 8x + 12x²\r\n" );
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document.write( "So we equate the first three terms respectively to those:\r\n" );
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document.write( "first term = 1 = 1  (so that's equal!)\r\n" );
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document.write( "second term = 4ax = 8x\r\n" );
document.write( "               4a = 8\r\n" );
document.write( "                a = 2\r\n" );
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document.write( "third term = (6a² + 4b)x² = 12x²\r\n" );
document.write( "                 6a² + 4b = 12\r\n" );
document.write( "               6(2)² + 4b = 12\r\n" );
document.write( "                 6∙4 + 4b = 12\r\n" );
document.write( "                  24 + 4b = 12\r\n" );
document.write( "                       4b = -12\r\n" );
document.write( "                        b = -3\r\n" );
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document.write( "Edwin

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