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Grazes
 2 years ago
Find the term that is a constant in the binomial expansion of...
Grazes
 2 years ago
Find the term that is a constant in the binomial expansion of...

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Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0\[(x ^{3}\frac{ 2 }{ x ^{2} })^{5}\]

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0\[\left(\begin{matrix}5 \\ U\end{matrix}\right)(x ^{3})^{nU}(\frac{ 2 }{ x ^{2} })^{U}\]

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.1Perfect. Now, were is \((x^{3})^{nU}\cdot\left(\dfrac{1}{x^{2}}\right)^U = x^{0}\)

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{ x ^{2} }{ 2 })^{U}\]?

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0nvm. I got it. Is 80 right?

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.1We can worry about the constants later. We just need to know which termn it is for now. \((x^{3})^{5}\cdot (x^{2})^{0} = x^{15}\) \((x^{3})^{4}\cdot (x^{2})^{1} = x^{10}\) \((x^{3})^{3}\cdot (x^{2})^{2} = x^{5}\) \((x^{3})^{2}\cdot (x^{2})^{3} = x^{0}\) \((x^{3})^{1}\cdot (x^{2})^{4} = x^{5}\) \((x^{3})^{0}\cdot (x^{2})^{5} = x^{10}\)

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0But set 3(5U)2U to zero and solve for U. Then you can plug it back in and get 80 oo

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.1Fair enough. It's not perfectly clear to me what "find the term" means. Does it mean completely define it (80) or just figure out which one it is (Term #4)? Excellent work!

Grazes
 2 years ago
Best ResponseYou've already chosen the best response.0It means to find the term that is a constant, rather than a coefficient and a variable(s)

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.1That doesn't clear it up at all. If you find a rock under a flower, do you necessarily know what color the rock is? What if it's dark out? It may seem a little silly, but exceptional clarity is a bit more difficult than allowing various assumptions. Let's see how it goes in this household. Mom: Steve, will you help me find my car keys? Steve: Sure. Where have you looked? M: In the kitchen and the bedroom. S: Okay, I'll go check the living room. {a few moments pass} S: Found them! M: Where were they? S: They're under the couch. {a few moments pass} M: Are you bringing the keys to me? S: You said "find" them. I found them. They're still under the couch. Maybe Steve was just being funny, but that doesn't mean Mom was being particularly clear.
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