document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96388>Question 96388</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618050485/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The question in the book is... Simplify the expression by combining like terms.\r<BR>\n" );
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document.write( "20.   p + 9q + 9 + 14P\r<BR>\n" );
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document.write( "24.   8(y + 2)+ y + 4\r<BR>\n" );
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document.write( "The book doesn't give examples of the above questions. Please help my daughter to understand combining like terms when ( ) are involved in the expression.  Thank you. - Laura P. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70177 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=70177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem tells you to combine like terms.  What it doesn't tell you in the instructions is<BR>\n" );
document.write( "the definition of \"like terms.\" Like terms contain the exact same variables (letters).<BR>\n" );
document.write( "For example: 3a and 2a are like terms because they have the letter \"a\" in common. 3a and 2 are<BR>\n" );
document.write( "not like terms because one has the letter \"a\" and the other does not have a letter at all.<BR>\n" );
document.write( "If a term does not have a letter at all, it is only like another term that does not have a <BR>\n" );
document.write( "letter either. For example 3 and 2 are like terms because neither has a letter.<BR>\n" );
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document.write( "Starting with this background, let's work problem 20. <BR>\n" );
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document.write( "Given:<BR>\n" );
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document.write( "p + 9q + 9 + 14p<BR>\n" );
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document.write( "(I'm going to assume that when you typed 14P you actually meant 14p. Technically a capital<BR>\n" );
document.write( "P could represent something different from a lower case p.)<BR>\n" );
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document.write( "Note that there are two like terms ... +p and +14p ... they are like because they both<BR>\n" );
document.write( "contain the just the single letter p. Therefore, they can be combined. p + 14p equals 15p.<BR>\n" );
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document.write( "So you can now delete p and +14p and replace them with 15p to get:<BR>\n" );
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document.write( "15p + 9q + 9<BR>\n" );
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document.write( "There are no other combinations that can be done because there are no \"like\" terms. One<BR>\n" );
document.write( "contains a p, one a q, and one has no associated letter.<BR>\n" );
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document.write( "Therefore, the answer to this problem is just 15p + 9q + 9<BR>\n" );
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document.write( "Now let's go to problem 24. This problem contains a minor \"twist.\" You are given:<BR>\n" );
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document.write( "8(y + 2) + y + 4<BR>\n" );
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document.write( "The \"twist\" is that you first have to do the distributed multiplication that is indicated<BR>\n" );
document.write( "by the parentheses. What is meant by 8(y + 2)? It means that you multiply 8 times each of<BR>\n" );
document.write( "the terms inside the parentheses. So you multiply 8 times y to get +8y and then you multiply<BR>\n" );
document.write( "8 times +2 to get +16. So you can replace 8(y + 2) with 8y + 16 and this makes the problem<BR>\n" );
document.write( "become:<BR>\n" );
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document.write( "8y + 16 + y + 4<BR>\n" );
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document.write( "Notice that 8y and +y are \"like\" terms because they both contain \"y.\" They can be combined<BR>\n" );
document.write( "by adding them. 8y + y = 9y. So replace the two terms with 9y and the problem reduces to:<BR>\n" );
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document.write( "9y + 16 + 4<BR>\n" );
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document.write( "Notice that the terms +16 and + 4 are like terms because neither has a letter. They are both<BR>\n" );
document.write( "just numbers so they can be added ... 16 + 4 = 20. So replace the 16 and 4 with their equivalent<BR>\n" );
document.write( "20 to make the problem become: 9y + 20<BR>\n" );
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document.write( "There are no \"like\" terms in these two terms ... one term contains a letter and the other<BR>\n" );
document.write( "does not.  Therefore, no other combining can be done and the answer to this last problem is<BR>\n" );
document.write( "just: 9y + 20<BR>\n" );
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document.write( "Hope this helps you to understand the problems a little better.<BR>\n" );
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document.write( " </SPAN>\n" );
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