document.write( "Question 1209116: Compute
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document.write( "1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2
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document.write( "without using a calculator. \n" );
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Algebra.Com's Answer #847694 by math_tutor2020(3817)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "1234567890 shows up repeatedly and 1234567891 is very close to the previous value. \n" ); document.write( "Let's assign a variable to them.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x = 1234567890 \n" ); document.write( "x+1 = 1234567890+1 \n" ); document.write( "x+1 = 1234567891\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "The original expression condenses to \n" ); document.write( "x^2 - 2x*x + (x+1)^2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Expand things out and simplify as much as possible. \n" ); document.write( "x^2 - 2x*x + (x+1)^2 \n" ); document.write( "x^2 - 2x^2 + x^2+2x+1 \n" ); document.write( "2x+1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "x^2 - 2x*x + (x+1)^2 fully simplifies to 2x+1.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Your original task of computing \n" ); document.write( "1234567890^2 - 2*1234567890*1234567890 + 1234567891^2 \n" ); document.write( "is equivalent to computing \n" ); document.write( "2*1234567890 + 1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "I'll let the student take over from here. \n" ); document.write( " \n" ); document.write( " |