document.write( "Question 696761: if p,q,r,s are any four consecutive terms of an A.P. Show that
\n" ); document.write( "p²-3q²+3r²-s² = 0 \n" ); document.write( "
Algebra.Com's Answer #429300 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "If d is the common difference in the A.P., then\r\n" );
document.write( "\r\n" );
document.write( "q = p+d,  r = p+2d,  s = p+3d\r\n" );
document.write( "\r\n" );
document.write( "p²-3q²+3r²-s² = \r\n" );
document.write( "\r\n" );
document.write( "p² - 3(q²-r²) - s² =\r\n" );
document.write( "\r\n" );
document.write( "(p²-s²) - 3(q²-r²) =\r\n" );
document.write( "\r\n" );
document.write( "Factor both parentheses as the difference of squares:\r\n" );
document.write( "\r\n" );
document.write( "[p-s][p+s] - 3[q-r][q+r] =\r\n" );
document.write( "\r\n" );
document.write( "Substitute q = p+d,  r = p+2d,  s = p+3d\r\n" );
document.write( "\r\n" );
document.write( "[p-(p+3d)][p+(p+3d)] - 3[(p+d)-(p+2d)][(p+d)+(p+2d)] =\r\n" );
document.write( "\r\n" );
document.write( "[p-p-3d][p+p+3d] - 3[p+d-p-2d][p+d+p+2d] =\r\n" );
document.write( "\r\n" );
document.write( "[-3d][2p+3d] - 3[-d][2p+3d] =\r\n" );
document.write( "\r\n" );
document.write( "-3d[2p+3d] + 3d[2p+3d] =\r\n" );
document.write( "\r\n" );
document.write( "-6dp -9d² + 6dp + 9d² =\r\n" );
document.write( "   \r\n" );
document.write( "          0\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );