document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191472>Question 191472</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the trinomial completely\r<BR>\n" );
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document.write( "7a^2+50ab+7b^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143681 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B50ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B50ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can see that the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the last term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7b%5E2 ALIGN=MIDDLE  ALT=\"7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the coefficients are 7 and 7 respectively.\r<BR>\n" );
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document.write( "Now multiply the first coefficient 7 and the last coefficient 7 to get 49. Now what two numbers multiply to 49 and add to the  middle coefficient 50? Let's list all of the factors of 49:\r<BR>\n" );
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document.write( "Factors of 49:\r<BR>\n" );
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document.write( "1,7\r<BR>\n" );
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document.write( "-1,-7 ...List the negative factors as well. This will allow us to find all possible combinations\r<BR>\n" );
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document.write( "These factors pair up and multiply to 49\r<BR>\n" );
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document.write( "1*49\r<BR>\n" );
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document.write( "7*7\r<BR>\n" );
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document.write( "(-1)*(-49)\r<BR>\n" );
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document.write( "(-7)*(-7)\r<BR>\n" );
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document.write( "note: remember two negative numbers multiplied together make a positive number\r<BR>\n" );
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document.write( "Now which of these pairs add to 50? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 50\r<BR>\n" );
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document.write( "<th>First Number</th><th>Second Number</th><th>Sum</th><tr><TD  align=\"center\">1</TD><TD  align=\"center\">49</TD><TD >1+49=50</TD></tr><tr><TD  align=\"center\">7</TD><TD  align=\"center\">7</TD><TD >7+7=14</TD></tr><tr><TD  align=\"center\">-1</TD><TD  align=\"center\">-49</TD><TD >-1+(-49)=-50</TD></tr><tr><TD  align=\"center\">-7</TD><TD  align=\"center\">-7</TD><TD >-7+(-7)=-14</TD></tr>\n" );
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document.write( "From this list we can see that 1 and 49 add up to 50 and multiply to 49\r<BR>\n" );
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document.write( "Now looking at the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B50ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B50ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50ab ALIGN=MIDDLE  ALT=\"50ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%2B49ab ALIGN=MIDDLE  ALT=\"ab%2B49ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > (notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab%2B49ab ALIGN=MIDDLE  ALT=\"ab%2B49ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > adds up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50ab ALIGN=MIDDLE  ALT=\"50ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So it is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50ab ALIGN=MIDDLE  ALT=\"50ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2Bhighlight%28ab%2B49ab%29%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2Bhighlight%28ab%2B49ab%29%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2Bab%2B49ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2Bab%2B49ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287a%5E2%2Bab%29%2B%2849ab%2B7b%5E2%29 ALIGN=MIDDLE  ALT=\"%287a%5E2%2Bab%29%2B%2849ab%2B7b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%287a%2Bb%29%2B7b%287a%2Bb%29 ALIGN=MIDDLE  ALT=\"a%287a%2Bb%29%2B7b%287a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group. Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7b ALIGN=MIDDLE  ALT=\"7b\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B7b%29%287a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28a%2B7b%29%287a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we have a common term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%2Bb ALIGN=MIDDLE  ALT=\"7a%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B1ab%2B49ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B1ab%2B49ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B7b%29%287a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28a%2B7b%29%287a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So this also means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B50ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B50ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B7b%29%287a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28a%2B7b%29%287a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B50ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B50ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B1ab%2B49ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B1ab%2B49ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "     Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7a%5E2%2B50ab%2B7b%5E2 ALIGN=MIDDLE  ALT=\"7a%5E2%2B50ab%2B7b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B7b%29%287a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28a%2B7b%29%287a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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