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How do you simplify #((4t^3)(2t))/(20t^2)# and what are the excluded values for the variable?

Answer 1

#((4t^3)(2t))/(20t^2)=color(green)(2/5t^2)#
#color(white)("XXXXXXXXXXXXXXXX")color(red)(t!=0)#

#color(red)(t=0)# must be excluded since this would result in an undefined expression value: #0/0#

#((4t^3)(2t))/(20t^2)# #color(white)("XXX")=((color(blue)(cancel(color(black)4))color(magenta)(cancel(color(black)(t^3))^t))(2t))/(color(blue)(cancel(color(black)(20))_5)color(magenta)(cancel(color(black)(t^2))))#

#color(white)("XXX")=(2t^2)/5#

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Answer 2

Nathan Axel

To simplify ((4t^3)(2t))/(20t^2), we can cancel out common factors. Simplifying the numerator, we have 8t^4. Simplifying the denominator, we have 20t^2. Cancelling out the common factor of 4, we get 2t^2. Therefore, the simplified expression is (8t^4)/(20t^2), which further simplifies to (2t^2)/5. The excluded value for the variable is t = 0, as division by zero is undefined.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.