A manufacturer of shipping boxes has a box shaped like a cube. The side length is
(5a + 4b)
. What is the volume of the box in terms of a and b?

- anonymous

- katieb

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- calculusxy

\[\large (5a + 4b)^3\]
it is like:
\[\large (5a+4b)(5a + 4b)(5a + 4b)\]
i would use FOIL so let's start with
\[\large (5a+4b)(5a+4b)\]

- calculusxy

\[\large (5a \times 5a) + (5a \times 4b) + (4b \times 5a) + (4b \times 4b)\]

- calculusxy

\[\large (5a + 4b)(25a^2 + 20ab + 20ba +16b^2)\]

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## More answers

- calculusxy

Continue using FOIL

- anonymous

whenever i watched the example video it had something to do with some kind of triangle not foil let me up load the video real quick

- anonymous

https://www.khanacademy.org/math/algebra2/polynomial_and_rational/binomial_theorem/v/pascals-triangle-binomial-theorem

- calculusxy

i think i understand this:
|dw:1442099987991:dw|

- calculusxy

the way that you get the numbers is by finding how many ways to get to the end. we have only went to the 3rd exponent because when trying to find the volume of cube, the side length is raised to the third power

- anonymous

ok im following so far i understood how to do the triangle thing but what i was confused about is how to apply that to the question i had

- calculusxy

we are going to use 1, 3, 3, 1 for the exponents to 5a and 4b
we will go from greatest to lowest (descending)
\[1(5)a^34b^0 + 3(5)a^24b^1 + 3(5)a^14b^2 + 1(5)a^04b^3\]

- calculusxy

the problme is whether i should multiply the 1, 3, 3, 1 to 4

- anonymous

i understand but why would u have to mutiply that in the video it just left everything like you have it in the post before this . i dont understand how your suppose to get the volume out of that but i did get how you got the (equation/ i guess you would call it that )

- calculusxy

you have a number front of the variable and that is causing some problems .. n the video it was only a variable

- calculusxy

*in

- anonymous

:/

- calculusxy

\[\large 5a^34b + 15a^212b + 15a12b^2 + 20b^3\]

- calculusxy

this is what might happen if you do multiply 1,3,3,1 to 4.

- anonymous

i just dont understand how you get all that down to one simply number ?

- calculusxy

\[1(5)a^3(1)4b^0 + 3(5)a^2(3)4b^1 + 3(5)a^1(3)4b^2 + 1(5)a^0(1)4b^3\]

- calculusxy

i basically used what the video had said.

- anonymous

oh i understand that i just dont understand how you get the volume out of that .

- calculusxy

i am completely new to this and i tried my best to help you out

- anonymous

thanks so much i really appreciate it . and i am too my teacher just sends me the video and expects me to just get it im going to look though my text book and see if i can find anything that will help me more !

- mathmate

@calculusxy @iloveyoukarsonlee
Recall that \(\Large (ab)^n = a^n\times b^n\)
so (5a+4b)^3
=\((1)(5a)^3+(3)(5a)^2(4b)+(3)(5a)(4b)^2+(1)(4b)^3\)
=\(125a^3+300a^2b+240ab^2+64b^3\)

- calculusxy

##### 1 Attachment

- calculusxy

that my was my work.. if u can understand my handwriting hopefully it can help u understand my process

- anonymous

yes that helps so much thank you both !!!

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