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FN
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 11:36
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^(x-2)) + y(a^(x-4)*b^(x-1)) + b^x, what is the value of yz?

(A) 24
(B) 30
(C) 36
(D) 42
(E) 50


please show working....



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zag1979
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 12:20
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The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 13:55
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hmm could you shed some light on this?

I figured out what y is, but had hard time figuring z....

basically I know that x =5, then I know that the coefficient of y will also be 5....figuring out z is the hard part...

zag1979
The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50
Show more
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FN
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 13:57
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actually this is a nice chart to remember whenever you have (a+b)^x...

depending on x..you can build out this chart...nice indeed....

can someone show how we can expand the pascal plot...to more than 6...
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richardj
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 16:16
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Just add the two numbers above each number when in the normal isosceles triangle design.

Or use the nCr formula.

Try looking up Pascal's triangle on a search engine on the internet.
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If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^ 06 Sep 2005, 22:09
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zag1979
The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50
Show more


Zag! Pretty d@mn good! I totally forgot that from high school. That makes these kind of problems a piece of cake.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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