Melody

$$\\(a+2b)^5=(2b)^5+5*(2b)^4*a+10*(2b)^3*a^2+10*(2b)^2*a^3+5*(2b)*a^4+a^5\\\\$$

I have done this with a binomial expansion.  You can simplify it yourself   

If you have questions then ask away  

atan(4.19)

just enter that into the home page calc  

nominal is a normal English word.

Let the squares that are cut out each be x by x cm       0<x<15

Now the volume of the prism will be

$$\\V=(30-2x)*(30-2x)*x\\\\
V=x(900-120x+4x^2)\\\\
V=4x^3-120x^2+900x\\\\
\frac{dV}{dx}=12x^2-240x+900\\\\
\frac{d^2V}{dx^2}=24x-240\\\\
$Stationary points will occur when $\frac{dV}{dx}=0\\\
12x^2-240x+900=0\\\\
x^2-20x+75=0\\\\
(x-5)(x-15)=0\\\\
x=5\qquad or \qquad x=15\\\\$$

$$\\When \;\;x=5\;\;\\\\
\frac{d^2V}{dx^2}=24*5-240<0\qquad Maximum \;\;at\;\; x=5\\\\
When \;\;x=15\;\;\\\\
$Volume is 0$\\\\
$So maximum volume occurs when x=5$\\\\
$Maximum volume $= V=(30-10)*(30-10)*5=2000cm^3\\\\$$

Think of negative numbers as cold numbers (like with temperature)

If you take cold out of a room then the room gets warmer.

so  - - = +

Have you done anything on imaginary numbers?

If not then the answer is "no soln" 

Arc sine is the same thing.

use.       asin

Hint. :)

2x^2y=-x^2y+3x^2y

and

-6x^2y=-1x^2y-5x^2y

Yes, I think it looks good so far, now you just have to get them both with a common denominator.

That will be  (5a-b)(a-2b)(2a+3b)

then you can add the numerators  

Well it is hard to read but it looks to me like x=7 will make the denominator of the first fraction = 0 and everyone knows that if you divide by 0 the universe will implode.

So that is not a good answer