document.write( "Question 715610: I need help with this question. Which are the first four terms in the expansion (2-3y) power of 8? \n" ); document.write( "

Algebra.Com's Answer #439535 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
There is a general formula that you were probably given, but probably makes no sense to you.
\n" ); document.write( "If your teacher wants it, write it the way it was given to you, but I will tell you what ideas I would use to get the answer (without worrying about formulas).
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\n" ); document.write( "Since the power is $\"8\"$ , there will be $\"8%2B1=9\"$ terms.
\n" ); document.write( "I could start with $\"2%5E8=256\"$ as a first term,
\n" ); document.write( "and end with $\"%28-3y%29%5E8\"$ as a last term,
\n" ); document.write( "and that is probably what's expected.
\n" ); document.write( "
\n" ); document.write( "All the terms will have combinations of powers of $\"2\"$
\n" ); document.write( "and powers of $\"%28-3y%29\"$ with exponents adding up to $\"8\"$ .
\n" ); document.write( "The exponents of $\"%28-3y%29\"$ increase from term to term, starting at zero and going up to $\"8\"$ .
\n" ); document.write( "The exponents of $\"2\"$ decrease from $\"8\"$ to zero.
\n" ); document.write( "The in-between terms, between the first term and the last term,
\n" ); document.write( "will also have combinatorial numbers as extra factors.
\n" ); document.write( "(There are many ways to write the symbols for combinatorial numbers,
\n" ); document.write( "but I do not know what way you would use in your class,
\n" ); document.write( "and I can only write combinatorial numbers in the form $\"%28matrix%282%2C1%2Cn%2Ck%29%29\"$ on this website).
\n" ); document.write( "Those combinatorials are all combinations of $\"8\"$
\n" ); document.write( "and the other number in the combination is one of the exponents.
\n" ); document.write( "Traditionally, it would be the exponent on $\"%28-3y%29\"$ .
\n" ); document.write( "(If you used the exponent of $\"2\"$ instead,
\n" ); document.write( "the symbol would look different,
\n" ); document.write( "but it would calculate as the same number).
\n" ); document.write( "
\n" ); document.write( "So term number $\"4\"$ would have
\n" ); document.write( " $\"%28-3y%29%5E%28%284-1%29%29=%28-3y%29%5E3=-27y%5E3\"$
\n" ); document.write( "with $\"3\"$ as the exponent for $\"%28-3y%29\"$ .
\n" ); document.write( "It would also have
\n" ); document.write( " $\"2%5E%28%288-3%29%29=2%5E5=32\"$ and
\n" ); document.write( "it would also have the combinatorial number
\n" ); document.write( " $\"%28matrix%282%2C1%2C8%2C3%29%29=8%2A7%2A6%2F1%2F2%2F3=+56\"$
\n" ); document.write( "So the fourth term is
\n" ); document.write( " $\"56%2A32%2A%28-27y%5E3%29=-48384y%5E3\"$
\n" ); document.write( "
\n" ); document.write( "The third term has $\"%28matrix%282%2C1%2C8%2C2%29%29=8%2A7%2F1%2F2=28\"$
\n" ); document.write( " $\"%28-3y%29%5E%28%283-1%29%29%29=%28-3y%29%5E2=9y%5E2\"$ and $\"2%5E%28%288-2%29%29%29=2%5E6=64\"$
\n" ); document.write( "So the third term is $\"28%2A64%2A%289y%5E2%29=16128y%5E2\"$
\n" ); document.write( "
\n" ); document.write( "The second term has $\"%28matrix%282%2C1%2C8%2C1%29%29=8%2F1=8\"$
\n" ); document.write( " $\"%28-3y%29%5E%28%282-1%29%29%29=%28-3y%29%5E1=-3y\"$ and $\"2%5E%28%288-1%29%29%29=2%5E7=128\"$
\n" ); document.write( "So the secondd term is $\"8%2A128%2A%28-3y%29=-3072y\"$
\n" ); document.write( "
\n" ); document.write( "Then the first four terms would be
\n" ); document.write( " $\"256-3072y%2B16128y%5E2-48384y%5E3\"$
\n" ); document.write( "If you have to \"show your work\", you could just write
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\n" ); document.write( "
\n" ); document.write( "A general formula for term number $\"k\"$ of the expansion of $\"%28a%2Bb%29%5En\"$
\n" ); document.write( "is $\"%28matrix%282%2C1%2Cn%2Ck%29%29%2Aa%5E%28%28n-k%2B1%29%29%2Ab%5E%28%28k-1%29%29\"$ \n" ); document.write( "

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