Question

I need help! I'll give you a medal! Question is attached!

Answer 1

hmmm actually, those aren't two cubic terms... hmmm

Answer 2

Yea, whatever i do i always get a^3-b^3. I don't know how to get the plus sign in there!

Answer 3

actually, yes they're
thus \(\bf \textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3 \\ \quad \\

a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad
(a-b)(a^2+ab+b^2)= a^3-b^3\)

Answer 4

Yes, hmm. But this still doesn't help because look at the problem. it starts off 3a^3-5b^3 and it ends with a^3+b^3! How??

Answer 5

right

Answer 6

hmmm I see... you're expected, pretty much, just to complete the 2nd factor in the cubic expansion, is all
so the "original binomial", based on the 1st term of \(3a^3-5b^3)\)
would have been then \(\bf (3a^3)^3-(5b^3)^3\implies (3a^3-5b^3)(\qquad \square? \qquad +\qquad \square?\qquad +\qquad \square ?\qquad )\)

Answer 7

or \(\bf (3a^3)^3-(5b^3)^3\implies (3a^3-5b^3)(\quad \square? \quad +\quad \square?\quad +\quad \square ?\quad )\)

Answer 8

But, how do i get the plus sign at the end?

Answer 9

hmmm

Answer 10

hmm I notice the first binomial is not a factor...

Answer 11

hmmm I gather it IS an equation.. ok

Answer 12

hold the mayo

Answer 13

Hahhaha, Thanks for bearing with me @jdoe0001

Answer 14

\(\large \begin{cases}
3a^3+{\color{red}{ \square}} a^3=a^3\implies &{\color{red}{\square }} =?\\
-5b^3+{\color{blue}{ \square}} b^3=b^3\implies &{\color{blue}{ \square }} =?
\end{cases}\)

what values would you get from that

Answer 15

-3
and for the second one i want to say +4

Answer 16

let's try that \(\bf 3a^3-3a^3 = 0\) and \(\bf -5b^3+4b^3= -1b^3\)
so.... is not -3 or +4

Answer 17

Hmm okay.
-2a^3 and +5a^3

Answer 18

well...
\(\bf 3a^3-2a^3= a^3\) well, that worked
and \(\bf -5b^3 + 5b^3 = 0\) so is not +5 on that one

Answer 19

-4?

Answer 20

let's see that one
\(\bf -5b^3-4b^3 = -9b^3\) no that one either

Answer 21

I have no idea anymore!

Answer 22

well... think about it... lemme put it this way then \(\bf \square b^3 -5b^3 = 1\implies \square = ?\)

Answer 23

6 then?