document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=410486>Question 410486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, Please help me solve this math problem...<BR>\n" );
document.write( "Directions are :factor each expression as a difference of squares.<BR>\n" );
document.write( "   4(x+y)^2 -(2y-z)^2<BR>\n" );
document.write( " my teacher told us to substitute, so i did :  a= xty,b= 2y-z<BR>\n" );
document.write( "                                               4(a)^2-(b)^2<BR>\n" );
document.write( "well i'm not sure i got the right answer and i'm still not 100% sure on what to do so if you could please try to explain it to me I would greatly appreciate it, Thank you XD </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #288635 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=288635\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> difference of squares:<BR>\n" );
document.write( "a^2 - b^2 = (a-b) * (a+b)\r<BR>\n" );
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document.write( "equation is:<BR>\n" );
document.write( "4*(x+y)^2 - (2y-z)^2\r<BR>\n" );
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document.write( "let a = 4*(x+y)^2 = 2^2*(x+y)^2 = (2*(x+y))^2 = (2x+2y)^2<BR>\n" );
document.write( "let b = (2y-z)\r<BR>\n" );
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document.write( "equation becomes:<BR>\n" );
document.write( "a^2 - b^2<BR>\n" );
document.write( "which is the difference of squares which is equivalent to:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2\r<BR>\n" );
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document.write( "a^2 - b^2 = (a-b) * (a+b)\r<BR>\n" );
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document.write( "this is equivalent to:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = ((2x+2y) - (2y-z)) * ((2x+2y) + (2y-z))<BR>\n" );
document.write( "because:<BR>\n" );
document.write( "(2x+2y) = a<BR>\n" );
document.write( "and:<BR>\n" );
document.write( "(2y-z) = b\r<BR>\n" );
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document.write( "this should be the answer you are looking for:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = ((2x+2y) - (2y-z)) * ((2x+2y) + (2y-z))\r<BR>\n" );
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document.write( "you should now be able to solve as follows:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = ((2x+2y) - (2y-z)) * ((2x+2y) + (2y-z))<BR>\n" );
document.write( "simplify expression on right of equal sign to get:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = (2x+2y -2y + z)) * (2x+2y + 2y-z)<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = (2x+z)) * (2x+4y-z)<BR>\n" );
document.write( "simplify further by multiplying expression on right of equal of sign to get:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = 4x^2 + 8xy + 4yz - z^2\r<BR>\n" );
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document.write( "this would be your answer after you've simplified as far as you can go:<BR>\n" );
document.write( "(2x+2y)^2 - (2y-z)^2 = 4x^2 + 8xy + 4yz - z^2\r<BR>\n" );
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document.write( "you would confirm by substituting random numbers for x, y, and z.\r<BR>\n" );
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document.write( "I used x = 3, y = 4, z = 5 and I got:<BR>\n" );
document.write( "187 = 187<BR>\n" );
document.write( "this confirmed it for me.\r<BR>\n" );
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document.write( "I substituted in the original expression of:<BR>\n" );
document.write( "4*(x+y)^2 - (2y-z)^2 to get 187\r<BR>\n" );
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document.write( "I then substituted in the final expression of:<BR>\n" );
document.write( "4x^2 + 8xy + 4yz - z^2 to also get 187\r<BR>\n" );
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document.write( "the key was to get the original expression to look like a^2 - b^2\r<BR>\n" );
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document.write( "that was done up top when I did the following:\r<BR>\n" );
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document.write( "let a = 4*(x+y)^2 = 2^2*(x+y)^2 = (2*(x+y))^2 = (2x+2y)^2<BR>\n" );
document.write( "let b = (2y-z)\r<BR>\n" );
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document.write( "the \"a\" part was the tricky part.\r<BR>\n" );
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document.write( "you needed to know that 4 = 2^2 and that 2^2 * (x+y)^2 = (2*(x+y)^2 = (2x+2y)^2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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