Question

A wooden garden tray with a base area of xy square inches is filled with soil up to a certain height. The tray contains (3xy + x2y2 + x3y2) cubic inches of soil. The height of the tray is represented by the expression.

Picture is attached! :)

Which expression below is the correct simplified form of the height of the tray?

Answer 1

Hint: factor out xy from the numerator

Answer 2

how do I do that? @jim_thompson5910

Answer 3

write each term in the numerator as something of this form xy*____

Answer 4

so x^2*y^2 turns into xy*____

fill in that blank

Answer 5

hhmmmm

Answer 6

xy^4?

Answer 7

x times ____ = x^2

what goes in the blank

Answer 8

2?

Answer 9

no
x * x

Answer 10

good

Answer 11

now fill in this blank

x^2*y^2 = xy*_____

Answer 12

xy?

Answer 13

yep

Answer 14

yay lol

Answer 15

x^3y^2 = xy*____

fill in that blank

Answer 16

xy^2?

Answer 17

no

Answer 18

xy^ 3?

Answer 19

x*_____ = x^3
y*_____ = y^2

Answer 20

x * x^2?

Answer 21

and y * y?

Answer 22

x^3y^2 = xy*____

Answer 23

so x^2y?

Answer 24

yep

Answer 25

3xy is the same as xy*3

Answer 26

so

3xy + x^2y^2 + x^3y^2

turns into

xy*3 + xy*xy + xy*x^2y

Answer 27

now you use the distributive property to factor out the common term of xy

which means

xy*3 + xy*xy + xy*x^2y

becomes

xy(3 + xy + x^2y)

Answer 28

if you were to distribute it back through and multiply, you would get 3xy + x^2y^2 + x^3y^2 back again

Answer 29

so why did I have you factor out xy ?

Answer 30

I have no idea lol

Answer 31

well 2 reasons

a) we were able to

b) the denominator has xy and ideally we want to cancel out the entire denominator with a matching term in the numerator (to make things as simple as possible)

Answer 32

the xy in the numerator and denominator cancel leaving us with

1(3 + xy + x^2y)
---------------
1

but that's the same as 3 + xy + x^2y

Answer 33

so that's the height

Answer 34

oh okay thanks alot for your help I understand now

Answer 35

you're welcome

Answer 36

=D medal 4 u lol

Answer 37

thx lol

Answer 38

wow u have ALOT of fans

Answer 39

hmm i guess so, but it's from over a long time

Answer 40

:P well cya laterz

Answer 41

you too