document.write( "Question 1200303: I need help factoring the two following expressions:
\n" ); document.write( " $\"+36%282a%5E2+-+3%29%5E2+-+44%282a%5E2+-+3%29+-+15+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+81%287a%2B3%29%5E4+-+72%287a%2B3%29%5E2+%2B+16\"$ \r
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Algebra.Com's Answer #834407 by ikleyn(52782) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Consider  81*(7a+3)^4 - 72*(7a+3)^2 + 16.\r\n" );
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document.write( "To simplify writing, introduce new variable u = (7a+3)^2.\r\n" );
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document.write( "Then the given expression takes the form  81u^2 -72u + 16.\r\n" );
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document.write( "From the first glance, it is clear that this expression is a full square\r\n" );
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document.write( "    81u^2 -72u + 16 = (9u - 4)^2.\r\n" );
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document.write( "Now return (7a+3)^2 instead of u into this formula.  You will get\r\n" );
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document.write( "    81*(7a+3)^4 - 72*(7a+3)^2 + 16 = 81u^2 -72u + 16 = (9u - 4)^2 = (9*(7a+3)^2-4)^2 = \r\n" );
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document.write( "    = ((21a+9)^2 - 4)^2.\r\n" );
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document.write( "Next, represent (21a+9)^2 - 4 as the difference of squares and factor it further\r\n" );
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document.write( "    (21a+9)^2 - 4 = (21a+9)^2 - 2^2 = ((21a+9)-2)*((21a+9)+2) = (21a+7)*(21a+11).\r\n" );
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document.write( "Therefore and finally,\r\n" );
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document.write( "    81*(7a+3)^4 - 72*(7a+3)^2 + 16 = (21a+7)^2*(21a+11)^2.    ANSWER\r\n" );
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document.write( "It is your desired factoring of the given original expression.\r\n" );
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