Question

Helpppp pleaseee >(easy question,easy medal)
trying to algebraically simplify this product..
(t^2+1)^3*(t+3)^5 ? do I just re-write as (cubed-root)t+1*5throot(t+3)?

Answer 1

I'm thinking what they want you to do is multiply everything out and then combine like terms.

Answer 2

it seems like multiplying out would give me some crazy polynomial?

Answer 3

Yea, I know. Usually they make you do the other way around, so I don't really know what they want...sorry. :(

Answer 4

(t^5 + 1^3)(t^5 + 3^5)

Answer 5

im terrible about remembering exponential rules...but can I do it that way or does it have to be multiplied completely out?... like.. (t^2+1)(t^2+1)(t^2+1)?... and so on..

Answer 6

Add the exponents of 2 and 3 then distribute the exponent outside of the parentasis to every term

Answer 7

@lahernan , no it doesn't because that's a different rule

Answer 8

Just do it the way @TemporalSorceress did it

Answer 9

well im not quite sure that's correct?

Answer 10

when you distribute the exponent it simplifies to\[(t ^{5} + 1^{3})(t ^{5} + 3^{5})\]

Answer 11

@wilder.monday That's is incorrect. You cannot distribute the exponent like that.

Answer 12

then how would you do it?

Answer 13

im evaluating it as a limit so .. im just trying to evaluate them as separate equations and then multiply them together...

Answer 14

I believe if I continue with what I did when simplifying it turns out to be \[t ^{15} + 3t ^{5} + 3^{5}\] and 3^5 simplifies further to 243

Answer 15

I think my instruction were a little confusing, im not trying to solve the polynomial im just trying to evaluate it to a simpler form...

Answer 16

may I see the material given?

Answer 17

the instructions are "Evaluate the limit and justify each step by indicating the appropriate limit law(s).
\[\lim_{t \rightarrow -1}(t ^{2}+1)^3(t+3)^5\]

Answer 18

this is using the multiplication limit law which states the limit as x goes to a of f(x)*g(x) = the limit as x goes to a of f(x) * the limit as x goes to a of g(x)

Answer 19

correct. which I understand that part, but I wasn't sure if I could just substitute -1 into t and then raise to the third power and do the same for the other side and then just raise to the 5th power if that was an accurate evaluation..?

Answer 20

u guys r doing great

Answer 21

\[\frac{ (t ^{5} + 1^{5})(t ^{5} + 3^{5}) }{ x - 1 }\]

Answer 22

@Noland__DeWitte thanks :)

Answer 23

welcome

Answer 24

I'm confused on how you derived that ?

Answer 25

its ok if u r confused u will get the hang of it @lahernan

Answer 26

\[\frac{ (t ^{2} + 1)^{3}(t + 3)^{5} }{ x - 1 }\]

Answer 27

give me a second to explain

Answer 28

original question: "Evaluate the limit and justify each step by indicating the appropriate limit law(s). lim t→−1 (t^2 +1)^3(t+3)^5

original is numerator and x - 1 is denominator. which was the last equation I did. when simplifying, the 1^3 stays as 1 and the 3^5 becomes 243.

now, plugging in 243 for x in x - 1, the limit comes out to be 242. if you plugged in the 1 for x in x - 1 the limit would be 0, which is not possible.

Answer 29

@lahernan

Answer 30

what do the squares mean?

Answer 31

oh nevermind. ok
I see what your saying.

Answer 32

it \[\lim_{t \rightarrow -1}\]

Answer 33

ok. well thank you very much for your help i'm going to print this out and regurgitate it and see if I can't let it soak in. .. :) thank you .

Answer 34

your welcome :) medal maybe?

Answer 35

sure thing

Answer 36

thanks!!

Answer 37

http://sketchtoy.com/64186775

Answer 38

This what you guys get?

Answer 39

I think so

Answer 40

The limit is 256.

Answer 41

thank you