Expand (w + x((2t)/T) + y((2t)/T)^2 + z((2t)/T)^3)^2 - Help Needed

[ashkash]

Homework Statement

Expand:
(w + x((2t)/T) + y((2t)/T)^2 + z((2t)/T)^3)^2

I need to expand this expression and have completely forgetten how to go about doing this. Any help would be appreciated. thanks.

Homework Equations

The Attempt at a Solution

 

[arildno]

Would you be able to expand the expression (a+b)^2?

 

[ashkash]

yes, it is a^2 + 2ab + b^2

 

[arildno]

Okay, so you could, for example start with defining a=(w+x(2t/T)+y(2t/T)^2) and b=z(2t/T)^3.

Can you set up what you get then?

 

[ashkash]

w^2 + z^2(2t/T)^2 + y^2(2t/T)^4 + 2wz(2t/T)^3 + 2xz(2t/T)^4 + 2yz(2t/T)^6 + z^2(2t/T)^6

is that correct?

 

[arildno]

No, do this PIECEWISE.
Just insert the expressions (with appropriate parantheses) on the a and b places before doing any further manipulations!

 

[ashkash]

ok so [(w+x(2t/T)+y(2t/T)^2) + (z(2t/T)^3)]^2 would be (a+b)^2

 

[arildno]

Right!
Use now the expansion formula you just cited for a and b!

 

[ashkash]

w^2 + 2wx(2t/T) + (x^2+2wy)(2t/T)^2 + (2xy+2wz)(2t/T)^3 + (y^2+2xz)(2t/T)^4 + (2yz+z^2)(2t/T)^6

Is this right?

 

[ashkash]

sorry, I think this should be correct now:

w^2 + 2wx(2t/T) + (x^2+2wy)(2t/T)^2 + (2xy+2wz)(2t/T)^3 + (y^2+2xz)(2t/T)^4 + 2yz(2t/T)^5 + z^2(2t/T)^6

Is this right?

 

[arildno]

Right!