document.write( "Question 1209802: Let A = x^4 + x^3 + x^2 + x + 1 and B = x^4 - x^3 + x^2 - x + 1. Simplify A + B. \n" ); document.write( "
Algebra.Com's Answer #850594 by CPhill(1987)\"\" \"About 
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Let's simplify the expression A + B.\r
\n" ); document.write( "\n" ); document.write( "Given:\r
\n" ); document.write( "\n" ); document.write( "* A = x^4 + x^3 + x^2 + x + 1
\n" ); document.write( "* B = x^4 - x^3 + x^2 - x + 1\r
\n" ); document.write( "\n" ); document.write( "We want to find A + B.\r
\n" ); document.write( "\n" ); document.write( "A + B = (x^4 + x^3 + x^2 + x + 1) + (x^4 - x^3 + x^2 - x + 1)\r
\n" ); document.write( "\n" ); document.write( "Now, combine like terms:\r
\n" ); document.write( "\n" ); document.write( "* x^4 + x^4 = 2x^4
\n" ); document.write( "* x^3 - x^3 = 0
\n" ); document.write( "* x^2 + x^2 = 2x^2
\n" ); document.write( "* x - x = 0
\n" ); document.write( "* 1 + 1 = 2\r
\n" ); document.write( "\n" ); document.write( "So, A + B = 2x^4 + 0x^3 + 2x^2 + 0x + 2\r
\n" ); document.write( "\n" ); document.write( "Therefore, A + B = 2x^4 + 2x^2 + 2\r
\n" ); document.write( "\n" ); document.write( "We can also factor out a 2:\r
\n" ); document.write( "\n" ); document.write( "A + B = 2(x^4 + x^2 + 1)\r
\n" ); document.write( "\n" ); document.write( "**Final Answer:** A + B = 2x^4 + 2x^2 + 2 or 2(x^4 + x^2 + 1)
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