document.write( "Question 47089: Please help me solve this problem (((X^2n+2x^n y^n+y^2n))) (((X^2n-2x^n y^n+y^2n))).I really appreciate any kind of help in solving. \n" ); document.write( "

Algebra.Com's Answer #31193 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "note that $\"x%5E%282n%29+=+%28x%5En%29%5E2\"$
\n" ); document.write( "and $\"y%5E%282n%29+=+%28y%5En%29%5E2\"$
\n" ); document.write( "now say $\"w+=+x%5En+\"$ and $\"z+=+y%5En+\"$
\n" ); document.write( "now
\n" ); document.write( " $\"%28w%5E2+%2B+2wz+%2B+z%5E2%29+%2A+%28w%5E2+-+2wz+%2B+z%5E2%29\"$
\n" ); document.write( "multiplying out, I get
\n" ); document.write( " $\"+w%5E4+%2B+z%5E4+-+2w%5E2+%2A+z%5E2\"$
\n" ); document.write( "now transform back
\n" ); document.write( " $\"w+=+x%5En+\"$
\n" ); document.write( " $\"z+=+y%5En+\"$
\n" ); document.write( " $\"x%5E%284n%29+%2B+z%5E%284n%29+-+2x%5E%282n%29%2A+y%5E%282n%29+\"$ answer
\n" ); document.write( "you can do a check by saying
\n" ); document.write( "n = 1
\n" ); document.write( "x = 2
\n" ); document.write( "y = 3
\n" ); document.write( "then
\n" ); document.write( "

\n" ); document.write( " $\"%284+%2B+12+%2B+9%29%2A+%284+-+12+%2B+9%29+=+25\"$
\n" ); document.write( " $\"25+=+25\"$
\n" ); document.write( " $\"x%5E%284n%29+%2B+z%5E%284n%29+-+2x%5E%282n%29%2A+y%5E%282n%29+\"$
\n" ); document.write( " $\"16+%2B+81+-+72+=+25\"$
\n" ); document.write( " $\"25+=+25\"$
\n" ); document.write( "checks OK
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );