document.write( "Question 1187212: Find the term that is independent of x in the expansion of $\"+%282+%2B+3%2Fx%5E2%29+%28x+-+2%2Fx%29%5E6+\"$ . \n" ); document.write( "

Algebra.Com's Answer #818320 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Expanded, $\"%28x+-+2%2Fx%29%5E6+\"$ is a polynomial with 7 terms.
\n" ); document.write( "It has terms in $\"X%5E6\"$ , $\"x%5E4\"$ , $\"x%5E2\"$ , $\"x%5E0\"$ (an independent term), $\"x%5E%28-2%29\"$ , $\"x%5E%28-4%29\"$ , y $\"x%5E%28-6%29\"$ .
\n" ); document.write( "The independent term in that polynomial is
\n" ); document.write( " $\"20%28x%5E3%29%28-2%2Fx%29%5E3=20%28-2%29%5E3=20%28-8%29=-160\"$ .
\n" ); document.write( "The term in $\"x%5E2\"$ in that polynomial is $\"15%28x%5E4%29%28-2%2Fx%29%5E2=15%284%29x%5E2=60x%5E2\"$
\n" ); document.write( "The independent term in the product $\"+%282+%2B+3%2Fx%5E2%29+%28x+-+2%2Fx%29%5E6+\"$ would be
\n" ); document.write( " $\"2%28-160%29%2B%283%2Fx%5E2%29%2860x%5E2%29=-320%2B3%2860%29=-320%2B180=-140\"$ \n" ); document.write( "

\n" );