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

  • Thread starter Thread starter ashkash
  • Start date Start date
  • Tags Tags
    Expansion
AI Thread Summary
The discussion focuses on expanding the expression (w + x((2t)/T) + y((2t)/T)^2 + z((2t)/T)^3)^2. Participants clarify the use of the expansion formula (a + b)^2, where a and b are defined as parts of the original expression. The correct expansion involves terms like w^2, 2wx(2t/T), and combinations of x, y, and z with appropriate powers of (2t/T). After several iterations, the final expansion is confirmed as 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. The discussion concludes with the correct expression being validated.
ashkash
Messages
31
Reaction score
0

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

 
Last edited:
Physics news on Phys.org
Would you be able to expand the expression (a+b)^2?
 
yes, it is a^2 + 2ab + b^2
 
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?
 
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?
 
No, do this PIECEWISE.
Just insert the expressions (with appropriate parantheses) on the a and b places before doing any further manipulations!
 
ok so [(w+x(2t/T)+y(2t/T)^2) + (z(2t/T)^3)]^2 would be (a+b)^2
 
Right!
Use now the expansion formula you just cited for a and b!
 
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
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
Right! :smile:
 
Back
Top