document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206241>Question 1206241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> So I really have no clue what to do for this question. The textbook asks for the coefficient of x. My thinking was that the coefficient should be 16, however, the answer is 96. The answer also calls for using Pascal's Triangle. <BR>\n" );
document.write( "(2x+2)^4<BR>\n" );
document.write( "Could someone please explain? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #843537 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=843537\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your looking at (2x + 2) ^ 4\r<BR>\n" );
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document.write( "this is the same as (2x + 2) ^ 2 * (2x + 2) ^ 2\r<BR>\n" );
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document.write( "(2x + 2) ^ 2 equals:<BR>\n" );
document.write( "(2x + 2) * (2x + 2) which equals:<BR>\n" );
document.write( "2x * (2x + 2) + 2 * (2x + 2) which equals:<BR>\n" );
document.write( "4x^2 + 4x + 4x + 4 which equals:<BR>\n" );
document.write( "4x^2 + 8x + 4.\r<BR>\n" );
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document.write( "(4x^2 + 8x + 4) ^ 2 equals:<BR>\n" );
document.write( "(4x^2 + 8x + 4) * (4x^2 + 8x + 4) which equals:<BR>\n" );
document.write( "4x^2 * (4x^2 + 8x + 4) + 8x * (4x^2 + 8x + 4) + 4 * (4x^2 + 8x + 4).\r<BR>\n" );
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document.write( "4x^2 * (4x^2 + 8x + 4) = 16x^4 + 32x^3 + 16x^2.<BR>\n" );
document.write( "8x * (4x^2 + 8x + 4) = 32x^3 + 64x^2 + 32x.<BR>\n" );
document.write( "4 * (4x^2 + 8x + 4) = 16x^2 + 32x + 16.\r<BR>\n" );
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document.write( "total is 16x^4 + 32x^3 + 16x^2 + 32x^3 + 64x^2 + 32x + 16x^2 + 32x + 16.\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "16x^4 + 64x^3 + 96x^2 + 64x + 16\r<BR>\n" );
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document.write( "i used an online binomial expansion calculator to confirm.<BR>\n" );
document.write( "it gave me the same answer.<BR>\n" );
document.write( "see below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/022501.jpg\">\r<BR>\n" );
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document.write( "the correct answer is 96, but that's the coefficient of the x^2 term, not the x term.\r<BR>\n" );
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document.write( "here's my worksheet from the formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/022502.jpg\">\r<BR>\n" );
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document.write( "here's the calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.symbolab.com/solver/binomial-expansion-calculator/expand%20%5Cleft(2x%2B2%5Cright)%5E%7B4%7D?or=input\" target = \"_blank\">https://www.symbolab.com/solver/binomial-expansion-calculator/expand%20%5Cleft(2x%2B2%5Cright)%5E%7B4%7D?or=input</a>\r<BR>\n" );
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document.write( "here's some references.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.le.ac.uk/users/dsgp1/COURSES/MATHSTAT/2binome.pdf\" target = \"_blank\">https://www.le.ac.uk/users/dsgp1/COURSES/MATHSTAT/2binome.pdf</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.math10.com/en/algebra/probabilities/binomial-theorem/binomial-theorem.html#:~:text=The%20Binomial%20Theorem%20Using%20Pascal's%20Triangle&text=(a%20%2B%20b)n%20%3D,st%20row%20of%20Pascal's%20triangle.\" target = \"_blank\">https://www.math10.com/en/algebra/probabilities/binomial-theorem/binomial-theorem.html#:~:text=The%20Binomial%20Theorem%20Using%20Pascal's%20Triangle&text=(a%20%2B%20b)n%20%3D,st%20row%20of%20Pascal's%20triangle.</a>\r<BR>\n" );
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