Mathematics
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OpenStudy (gabylovesyou):
Choose the correct simplification of the expression (6x2y)2(y2)3.
12x4y8
36x4y5
36x4y8
12x2y7
Question 14 (Multiple Choice Worth 5 points)
[7.02] Choose the correct sum of the polynomials (6x3 − 8x − 5) + (3x3 + 6x + 2).
9x3 − 2x − 3
3x3 + 2x + 3
3x3 − 2x − 3
9x3 + 14x + 3

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jimthompson5910 (jim_thompson5910):
(6x^2)^2 simplifies to what

OpenStudy (gabylovesyou):
36x^4

jimthompson5910 (jim_thompson5910):
very good

jimthompson5910 (jim_thompson5910):
oh sry there was a y in there as well

OpenStudy (gabylovesyou):
yes

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jimthompson5910 (jim_thompson5910):
(6x^2y)^2 turns into 3x^4y^2

OpenStudy (gabylovesyou):
how ?

jimthompson5910 (jim_thompson5910):
(y^2)^3 = y^6 because you multiply exponents
so
(6x^2y)^2*(y^2)^3
turns into
36x^4y^2*y^6
then you add the exponents for the y terms to get 2+6 = 8

jimthompson5910 (jim_thompson5910):
because y is the same as y^1

jimthompson5910 (jim_thompson5910):
then you multiply exponents

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jimthompson5910 (jim_thompson5910):
afterwards
36x^4y^2*y^6
turns into
36x^4y^8

jimthompson5910 (jim_thompson5910):
do you see how I got this?

OpenStudy (gabylovesyou):
kinda.. how did u simplify(6x^2y)^2

jimthompson5910 (jim_thompson5910):
here's another way to see it

jimthompson5910 (jim_thompson5910):
(6x^2y)^2
(6x^2y)*(6x^2y)
(6*6)*(x^2*x^2)*(y*y)
36x^4y^2

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jimthompson5910 (jim_thompson5910):
So (6x^2y)^2 simplifies to 36x^4y^2

OpenStudy (gabylovesyou):
oh ok ! got it!

OpenStudy (gabylovesyou):
the answer is 36x4y8

OpenStudy (gabylovesyou):
thank you

jimthompson5910 (jim_thompson5910):
yes it is

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jimthompson5910 (jim_thompson5910):
yw

OpenStudy (gabylovesyou):
oh wait i forgot the other question lol

jimthompson5910 (jim_thompson5910):
6x^3 + 3x^3 = ???

OpenStudy (gabylovesyou):
9x6?

jimthompson5910 (jim_thompson5910):
no you don't add the exponents

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jimthompson5910 (jim_thompson5910):
just the coefficients

OpenStudy (gabylovesyou):
ohhhh so i leave 3?

jimthompson5910 (jim_thompson5910):
-8x+6x = ???

jimthompson5910 (jim_thompson5910):
yes

OpenStudy (gabylovesyou):
-2x

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jimthompson5910 (jim_thompson5910):
-5 + 2 = ??

OpenStudy (gabylovesyou):
-3

jimthompson5910 (jim_thompson5910):
put this all together to get
9x^3 - 2x - 3

OpenStudy (gabylovesyou):
thank you!!!!

jimthompson5910 (jim_thompson5910):
you're welcome