# Expansion Question

1. Jan 21, 2007

### ashkash

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

3. The attempt at a solution

Last edited: Jan 21, 2007
2. Jan 21, 2007

### arildno

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

3. Jan 21, 2007

### ashkash

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

4. Jan 21, 2007

### 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?

5. Jan 21, 2007

### 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?

6. Jan 21, 2007

### arildno

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

7. Jan 21, 2007

### ashkash

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

8. Jan 21, 2007

### arildno

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

9. Jan 21, 2007

### 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?

10. Jan 21, 2007

### 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?

11. Jan 22, 2007

Right!