document.write( "Question 714337: I would like to know how to factor 64x^3-27y^3. Also, i need to be provided with the steps to getting to my solution as well! Thank you \n" ); document.write( "
Algebra.Com's Answer #438777 by AnlytcPhil(1808)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "We memorize the way to factor the sum or the difference of cubes:\r\n" );
document.write( "\r\n" );
document.write( "A³ ± B³ = (A ± B)(A² ∓ AB + B²)\r\n" );
document.write( "\r\n" );
document.write( "That is, the sum of two cubes factors like this:\r\n" );
document.write( "\r\n" );
document.write( "A³ + B³ = (A + B)(A² - AB + B²)\r\n" );
document.write( "\r\n" );
document.write( "And the difference of two cubes factors like this:\r\n" );
document.write( "\r\n" );
document.write( "A³ - B³ = (A - B)(A² + AB + B²)\r\n" );
document.write( "\r\n" );
document.write( "Be sure to memorize these. \r\n" );
document.write( "\r\n" );
document.write( "Your problem is\r\n" );
document.write( "\r\n" );
document.write( "64x³ - 27y³\r\n" );
document.write( "\r\n" );
document.write( "since 64 = 4³ and 27 = 3³, we can write that as\r\n" );
document.write( "\r\n" );
document.write( "(4x)³ - (3y)³\r\n" );
document.write( "\r\n" );
document.write( "So we substitute A = 4x  and B = 3y  in\r\n" );
document.write( "\r\n" );
document.write( "A³ - B³ = (A - B)[A² + AB + B²]\r\n" );
document.write( "\r\n" );
document.write( "(4x)³ - (3y)³ = (4x - 3y)[(4x)² + (4x)(3y) + (3y)²]\r\n" );
document.write( "\r\n" );
document.write( "Then we simplify the bracket expression:\r\n" );
document.write( "\r\n" );
document.write( "              = (4x - 3y)[16x² + 12xy + 9y²]\r\n" );
document.write( " \r\n" );
document.write( "              = (4x - 3y)(16x² + 12xy + 9y²)\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );