document.write( "Question 1209116: Compute
\n" ); document.write( "1234567890^2 - 2 \cdot 1234567890 \cdot 1234567890 + 1234567891^2
\n" ); document.write( "without using a calculator.
\n" ); document.write( "

Algebra.Com's Answer #847694 by math_tutor2020(3817)\"\" \"About 
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( "
\n" );