document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204943>Question 1204943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How is (-3/4(-8a)+(-3/4)(-12) equivalent to both -3/4(-8a-12) and 6a+9?<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 #841500 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=841500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You should be careful about the parenthesis placement. <BR>\n" );
document.write( "If in doubt, use a calculator or CAS (computer algebra system) to validate the input.<BR>\n" );
document.write( "A rule of thumb: There should be the same number of opening parenthesis \"(\" compared to the number of closing parenthesis \")\". Otherwise things are unbalanced.\r<BR>\n" );
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document.write( "It appears you're asking how is (-3/4)(-8a)+(-3/4)(-12) equivalent to both (-3/4)(-8a-12) and 6a+9\r<BR>\n" );
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document.write( "The simple answer is <font color=red>distributive property</font><BR>\n" );
document.write( "p(q+r) = p*q + p*r<BR>\n" );
document.write( "Multiply the outer 'p' with each term inside.\r<BR>\n" );
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document.write( "For example,<BR>\n" );
document.write( "2(3+4) = 2*3+2*4 = 6+8 = 14<BR>\n" );
document.write( "and using PEMDAS we find that<BR>\n" );
document.write( "2(3+4) = 2*(7) = 14<BR>\n" );
document.write( "This is one example using numbers to verify the distributive property works. \r<BR>\n" );
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document.write( "Another example<BR>\n" );
document.write( "3*(103) <BR>\n" );
document.write( "= 3*(100+3) <BR>\n" );
document.write( "= 3*100 + 3*3<BR>\n" );
document.write( "= 300 + 9<BR>\n" );
document.write( "= 309<BR>\n" );
document.write( "In short, 3*103 = 309\r<BR>\n" );
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document.write( "One more example with numbers only<BR>\n" );
document.write( "7*(215) <BR>\n" );
document.write( "= 7*(200+10+5) <BR>\n" );
document.write( "= 7*200 + 7*10 + 7*5<BR>\n" );
document.write( "= 1400 + 70 + 35<BR>\n" );
document.write( "= 1400 + 105<BR>\n" );
document.write( "= 1505<BR>\n" );
document.write( "In short, 7*215 = 1505\r<BR>\n" );
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document.write( "Now let's look at a few examples involving variables<BR>\n" );
document.write( "4*(3x+5) = 4*3x + 4*5 = 12x + 20<BR>\n" );
document.write( "and<BR>\n" );
document.write( "7w*(9w+2) = 7w*9w + 7w*2 = 63w^2 + 14w<BR>\n" );
document.write( "and<BR>\n" );
document.write( "11(3+6p) = 11*3+11*6p = 33+66p = 66p+33<BR>\n" );
document.write( "I encourage you to try other examples on your own.\r<BR>\n" );
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document.write( "Why can we extend the distributive property from numbers only to variables? Because variables are placeholders for numbers. It's a more abstract version. <BR>\n" );
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