document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1016732>Question 1016732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Expand and simplify:<BR>\n" );
document.write( "(x+y-z) (x-y+z)\r<BR>\n" );
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document.write( "Could you please have a step by step solution? It's really hard to me, thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #633128 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=633128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x + y - z) * (x - y + z)\r<BR>\n" );
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document.write( "you use the distributive law of multiplication.<BR>\n" );
document.write( "that law says that each element in the multiplier needs to multiply each element in the multiplicand exactly one time.\r<BR>\n" );
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document.write( "you break your multiplication up as follows:\r<BR>\n" );
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document.write( "(x + y - z) * (x - y + z) equals:\r<BR>\n" );
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document.write( "x * (x - y + z) + y * (x - y + z) - z * (x - y + z) <BR>\n" );
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document.write( "x * (x - y + z) is equal to x^2 - xy + xz<BR>\n" );
document.write( "y * (x - y + z) is equal to xy - y^2 + yz<BR>\n" );
document.write( "- z * (x - y + z) is equal to -xz + yz - z^2\r<BR>\n" );
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document.write( "when you put them all together, you get:\r<BR>\n" );
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document.write( "x * (x - y + z) + y * (x - y + z) - z * (x - y + z) is equal to:\r<BR>\n" );
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document.write( "x^2 - xy + xz + xy - y^2 + yz - xz + yz - z^2\r<BR>\n" );
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document.write( "when you combine like terms, you get:\r<BR>\n" );
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document.write( "- xy and +xy cancel out.<BR>\n" );
document.write( "+ xz and -xz cancel out.<BR>\n" );
document.write( "+ yz and + yz becomes 2yz.\r<BR>\n" );
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document.write( "you are left with x^2 - y^2 + 2yz - z^2\r<BR>\n" );
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document.write( "that's your final expression.\r<BR>\n" );
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document.write( "you can confirm you did this correctly by assigning random values to x,y, and z.\r<BR>\n" );
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document.write( "i assigned x = 2, y = 3, z = 4.\r<BR>\n" );
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document.write( "the original expression is:\r<BR>\n" );
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document.write( "(x + y - z) * (x - y + z)\r<BR>\n" );
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document.write( "after assigning values, the expression becomes (2 + 3 - 4) * (2 - 3 + 4).<BR>\n" );
document.write( "this becomes 1 * 3 which is equal to 3.\r<BR>\n" );
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document.write( "the final expression is:\r<BR>\n" );
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document.write( "x^2 - y^2 + 2yz - z^2\r<BR>\n" );
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document.write( "after assigning values, the expression becomes 2^2 - 3^2 + 2*3*4 - 4^2.<BR>\n" );
document.write( "this becomes 4 - 9 + 24 - 16 which is equal to 3.\r<BR>\n" );
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document.write( "original expression and final expression give the same answer, therefore they are equivalent.\r<BR>\n" );
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document.write( "solution looks good.\r<BR>\n" );
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document.write( "your solution is:\r<BR>\n" );
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document.write( "(x + y - z) * (x - y + z) = x^2 - y^2 + 2yz - z^2\r<BR>\n" );
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document.write( " </SPAN>\n" );
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