document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=854249>Question 854249</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me with this question. Thank you so much\r<BR>\n" );
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document.write( "Factorise each of the following expressions, that is, write them as a product.\r<BR>\n" );
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document.write( "a.)8b^3a^2-4a^4b^3+16a^5b^5<BR>\n" );
document.write( "b.)4x^2(a+b)+4x^2(a-b) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #514531 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=514531\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll do part b first.\r<BR>\n" );
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document.write( "4x^2(a + b) + 4x^2(a - b)<BR>\n" );
document.write( "simplify by performing the indicted operations to get:<BR>\n" );
document.write( "4x^2*a + 4x^2*b + 4x^2*a - 4x^2*b<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "8x^2*a\r<BR>\n" );
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document.write( "that should be your answer.<BR>\n" );
document.write( "the 4x^2*a and the 4x^2*a add together to get 8x^2*a.<BR>\n" );
document.write( "the 4x^2*b and the -4x^2*b cancel each other out.\r<BR>\n" );
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document.write( "i'll do part a next as best i can determine what they are looking for.\r<BR>\n" );
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document.write( "8*b^3*a^2-4*a^4*b^3+16*a^5*b^5<BR>\n" );
document.write( "factor out a 4 to get:<BR>\n" );
document.write( "4 * (2*b^3*a^2 - a^4*b^3 + 4*a^5*b^5)<BR>\n" );
document.write( "factor out an a^2 to get:<BR>\n" );
document.write( "4*a^2 * (2*b^3 - a^2*b^3 + 4*a^3*b^5)<BR>\n" );
document.write( "factor out a b^3 to get:<BR>\n" );
document.write( "4*a^2*b^3 * (2 - a^2 + 4*a^3*b^2)\r<BR>\n" );
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document.write( "you could stop there, but there is a little more factoring that can be done as follows:\r<BR>\n" );
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document.write( "reorder the terms within the parentheses to get:<BR>\n" );
document.write( "4*a^2*b^3 * (4*a^3*b^2 - a^2 + 2)<BR>\n" );
document.write( "factor out an a^2 from the first 2 terms in the parentheses to get:<BR>\n" );
document.write( "4*a^2*b^3 * (a^2 * ((4*a*b^2 - 1) + 2)\r<BR>\n" );
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document.write( "i think that's about as far as you can go.<BR>\n" );
document.write( "it helps to confirm if the final expression is equivalent to the initial expression.\r<BR>\n" );
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document.write( "a way to do that is to give random values to a and b and see if the initial expression gives you the same answer as the final expression.\r<BR>\n" );
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document.write( "i chose a = 2 and b = 3.\r<BR>\n" );
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document.write( "using those values, the initial expression of:<BR>\n" );
document.write( "8*b^3*a^2-4*a^4*b^3+16*a^5*b^5 becomes:<BR>\n" );
document.write( "8*3^3*2^2 - 4*2^4*3^2 + 16*2^5*3^5 which simplifies to:<BR>\n" );
document.write( "864 - 1728 + 124416 which is equal to 123552.\r<BR>\n" );
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document.write( "the final expression of:<BR>\n" );
document.write( "4*a^2*b^3 * ((a^2 * (4*ab^2 - 1) + 2) becomes:<BR>\n" );
document.write( "(4*2^2*3^3) * ((2^2*(4*2*3^2 - 1) + 2) which becomes:<BR>\n" );
document.write( "432 * (4*(71) + 2) which becomes:<BR>\n" );
document.write( "432 * (284 + 2) which becomes:<BR>\n" );
document.write( "432 * 286 which becomes 123552.\r<BR>\n" );
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document.write( "since both expressions give the same answer, this is a good sign that the final expression is equivalent to the original expression.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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