Expand And Simplify (x-1/x)^4.?

Question

I believe its in relation to pascals triangle, but this has thrown me a little.

Answer 1

Expanding (x-1/x)^4 is a question on the binomial theorem.
The expansion is of the form:
Ax^4 - Bx^3(1/x) + Cx^2(1/x^2) - Dx(1/x^3) + E(1/x^4)
where are A, B, C, D and E are integers.
The binomial theorem gives formulae for these numbers, but they can also be obtained from Pascal's triange (see Wikipedia) where the fifth row gives A = 1, B = 4, C = 6, D = 4, E = 1.
You can then simplify the individual terms of the expansion.

Answer 2

Use the Pascal's and find the coefficient for the 4-th power as: 1-4-6-4-1. To avoid misunderstanding, I change the x's into y's
such the problem becomes (y-1/y)^4. The result will be:
1 of y^4 minus 4 of y^3x(1/y) plus 6 of y^2x(1/y)^2 minus 4 of yx(1/y)^3 plus 1 of (1/y)^4. It can be simplified as:
y^4 - 4xy^2 + 6 - 4/(y^2) + 1/y^4

Answer 3

[(x - 1) divided by (1 - x)] to the power of 4

eg x = 3

3 - 1 divided by 1 - 3 to the power of 4

(2 / -2) ^ 4

-1 ^4 (working -1 x -1 x -1 x -1)

= 1

to find fourth power on scientic calc look for button which says Yx its usually next to the buttons that have x2 & x3

Answer 4

Could you clarify...

should there be brackets round the x-1 or is it just the 1 being divided by the x?