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 2 years ago
Explain, in complete sentences, how you would expand (3x + 7y)^4 using Pascal’s Triangle.
I got 3x^4+84x^3y+126x^2y^2+84xy^3+7y^4. Can anyone verify to see if this is correct? :) Thank you very much.
 2 years ago
Explain, in complete sentences, how you would expand (3x + 7y)^4 using Pascal’s Triangle. I got 3x^4+84x^3y+126x^2y^2+84xy^3+7y^4. Can anyone verify to see if this is correct? :) Thank you very much.

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Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0Oh okay, can you show me what I did wrong?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3what is the 5th row of pascal's triangle?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3yes, and those will be your coefficients now what are your terms?

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0x^4 + x^3y + x^2y^2 + xy^3 + y^4

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3no, you have ignored the coefficients in the terms themselves they must remain...

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.01x^4+4x^3y+6x^2y^2+4xy^3+1y^4 ?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3the terms are 3x and 7y so you have 1 4 6 4 1 1(3x)^4(7y)^0+4(3x)^3(7y)^1+6(3x)^2(7y)^2+4(3x)^1(7y)^3+1(3x)^0(7y)^4

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0When I combine everything I still get what I still got from up above. o.O 1st term 3x^4 2nd term 84x^3y 3rd term 126x^2y^2 4th term 84xy^3 5th term= 7y^4 Am I combining some of these terms wrong?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3did you try to include the coefficients from pascals triangle yet or no? because what you have is not quite right any way I can slice it, but it's closer

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0I included the 1,4,6,4,1 into the multiplying.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3let's just look at the terms first without the coefficients then to see where you went wrong

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3terms:\[\begin{array}91^{st}= (3x)^4(7y)^0=3^4x^4=81x^4\\2^{nd}=(3x)^3(7y)^1=3^3x^3\cdot7^1y^1=567x^3y^1\\3^{rd}=(3x)^2(7y)^2\\4^{th}=(3x)^1(7y)^3\\5^{th}=(3x)^0(7y)^4\end{array}\]you failed to distribute the exponents properly... I will continue but this should be enough to see your mistake we then put in the coefficients from Pascal's triangle at the end and add it all up

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0Oh I forgot to use the exponent on the numbers too. So it should actually be 81x^4+567x^3y^1+441x^2y^2+1029x^1y^3+2401 correct? :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3\[\begin{array}91^{st}= (3x)^4(7y)^0=3^4x^4=81x^4\\2^{nd}=(3x)^3(7y)^1=3^3x^3\cdot7^1y^1=567x^3y^1\\3^{rd}=(3x)^2(7y)^2=3^2x^2\cdot7^2y^2=441x^2y^2\\4^{th}=(3x)^1(7y)^3=3x\cdot7^3y^3=1029xy^3\\5^{th}=(3x)^0(7y)^4=7^4y^4=2401y^4\end{array}\]yeah but you forgot the y^4 at the end ;)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3and I wouldn't write them all summed up like that yet until we use the right coefficients from the triangle

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0oh yeah careless mistake there :) Wait we still have to multiply this with 1,4,6,4,1 right?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3yes, by the 5th row of the triangle we have the coefficients of the terms as\[1(1^{st})+4(2^{nd})+6(3^{rd})+4(4^{th})+1(5^{th})\]

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0K so the final problem would be 81x^4+2268x^3y+2646x^2y^2+4116xy^3+2401 right? :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3the second coefficient is wrong, but that is due to a typo I made above I can see find it and fix it! that should be your effort in this :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3besides that everything else is correct though

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0It should be 756x^3y right?

robtobey
 2 years ago
Best ResponseYou've already chosen the best response.0\[(3 x+7 y)^4=81 x^4+756 x^3 y+2646 x^2 y^2+4116 x y^3+2401 y^4 \]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3http://www.wolframalpha.com/input/?i=expand%20(3x%20%2B%207y)%5E4%20

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0Thx a ton @TuringTest for helping me with this problem :)

Loujoelou
 2 years ago
Best ResponseYou've already chosen the best response.0I know wolframalpha but I wanted to not use anything like that on my test so yeah :) Thx!

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3Yeah I just gave it for you to check your work. You should never rely on it; it is wrong more often than you would probably think at first.

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.3...and you're very welcome!
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