document.write( "Question 28143: Question: Use a method to determine the LCM for
\n" ); document.write( "(9x^3-9x^2-18x) and (6x^5-24x^4+24x^3)
\n" ); document.write( "What is the LCM?
\n" ); document.write( "Please help! Thank you! \n" ); document.write( "
Algebra.Com's Answer #15334 by sdmmadam@yahoo.com(530)\"\" \"About 
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Question: Use a method to determine the LCM for
\n" ); document.write( "(9x^3-9x^2-18x) and (6x^5-24x^4+24x^3)
\n" ); document.write( "What is the LCM? \r
\n" ); document.write( "\n" ); document.write( "(9x^3-9x^2-18x)----(1)
\n" ); document.write( "=9x(x^2-x-2)
\n" ); document.write( "=9x(x-2)(x+1)----(*)(on factorising)\r
\n" ); document.write( "\n" ); document.write( "(6x^5-24x^4+24x^3)----(2)
\n" ); document.write( "=6x^3(x^2-4x+4)
\n" ); document.write( "=6x^3(x-2)(x-2)----(**)(on factorising)
\n" ); document.write( "lcm of (1) and (2) is lcm of (*) and (**)
\n" ); document.write( "Therefore lcm of 9x(x-2)(x+1)and 6x^3(x-2)(x-2)is given by
\n" ); document.write( "18x^3(x+1)(x-2)^2
\n" ); document.write( "Answer:18x^3(x+1)(x-2)^2\r
\n" ); document.write( "\n" ); document.write( "Note: How?
\n" ); document.write( "the lcm of x and x^3 is x^3
\n" ); document.write( "the lcm of 9=3X3 and 6=2X3 is 3X2X3 = 18
\n" ); document.write( "(the common factor 3 and then the loose factor 3 of the first and the loose factor 2 of the second)
\n" ); document.write( "Similarly for the lcm of (x-2)(x+1)and (x-2)(x-2)(the common factor (x-2) and then the loose factor (x+1)of the first and the loose factor (x-2) of the second)\r
\n" ); document.write( "\n" ); document.write( "Note:
\n" ); document.write( "(x^2-x-2)=[x^2+(-2x+x)-2]
\n" ); document.write( "[splitting the mid term into two parts in such a way that their sum is the mid term and their product is the product of the square term and the constant term.
\n" ); document.write( "Now -x= +(-2x+x) and (-2x)X(x) = -2x^2 = (x^2)X(-2)]
\n" ); document.write( "=[(x^2-2x)+(x-2)]
\n" ); document.write( "=[x(x-2)+1(x-2)]
\n" ); document.write( "=[xp+p](where p = (x-2)}
\n" ); document.write( "=p(x+1)
\n" ); document.write( "=(x-2)(x+1)
\n" ); document.write( "Note:(x^2-4x+4)
\n" ); document.write( "= (x)^2-2(x)(2) + (2)^2 [in the form (a)^2 -2ab+(b)^2 = (a-b)^2]
\n" ); document.write( "=(x-2)^2
\n" ); document.write( "=(x-2)(x-2)
\n" ); document.write( "You may factorise in the first note form method too.
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