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Suppose that \(\Join\) is an operation defined by \(x \Join y = (x+2)(y-3)\). What is \(((t) \Join (t+2)) - ((t+1) \Join (t+1))\)?

 Dec 2, 2020
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(Sorry I do not have a picture or key for that operation thingy you have but I'll try my best)

 

so if |><| means (x+2)(y-3) and we're trying to find ((t)|><|(t+2))-((t+1)|><|(t+1)), first we must expand it

((t)|><|(t+2)) would have t represent x and (t+2) represent y so (t+2)((t+2)-3). We can expand that to t^2+t-2

Next we have ((t+1)|><|(t+1)) We do the same thing (t+1+2)(t+1-3) which expands to t^2+t-6.

(t^2+t-2)-(t^2+t-6)=-8

Pretty sure that's correct

 Dec 2, 2020

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