document.write( "Question 1094991: Can someone help me to solve this?
\n" ); document.write( "When (1-3x)^n is expanded, the coefficient of x^2 is 90. How to find n algebraically? \n" ); document.write( "

Algebra.Com's Answer #709550 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!
Can someone help me to solve this?
\n" ); document.write( "When (1-3x)^n is expanded, the coefficient of x^2 is 90. How to find n algebraically?
\n" ); document.write( "

This is saying that there’s a specific term that’s 90x²\r\n" );
document.write( "\r\n" );
document.write( "The formula to find a SPECIFIC term in a BINOMIAL expansion is: \r\n" );
document.write( ", where r = term number \r\n" );
document.write( " ------ Substituting 1 for a, and - 3x for b\r\n" );
document.write( " ------- Replacing  with 1 as 1 raised to ANY POWER equals 1  \r\n" );
document.write( "\r\n" );
document.write( "From this, we can see that:  \r\n" );
document.write( "Therefore, r – 1 MUST = 2 \r\n" );
document.write( "r, or term number with the term 90x² = 2 + 1 = 3\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since r = 3, then  becomes:\r\n" );
document.write( "                   \r\n" );
document.write( "                   \r\n" );
document.write( "                   \r\n" );
document.write( "                  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( " ------- Cross-multiplying\r\n" );
document.write( "n(n – 1) = 20\r\n" );
document.write( "Observing the above equation, it's clear that: , as 5(5 – 1), or 5(4) = 20.\r\n" );
document.write( "You could've also distributed the above equation, and solve the formed quadratic by FACTORING to get the same result: n = 5.

\n" ); document.write( "

\n" );