- #1

dynamic998

find the third term of the expansion (2x-y)to the third power.

I know u have to do the things with the combinations but all i get is 20xy² but the answer is 6xy². Can anyone help?

- Thread starter dynamic998
- Start date

- #1

dynamic998

find the third term of the expansion (2x-y)to the third power.

I know u have to do the things with the combinations but all i get is 20xy² but the answer is 6xy². Can anyone help?

- #2

- 313

- 0

I think you mean to find the 3rd term in descending powers of xfind the third term of the expansion (2x-y)to the third power.

I know u have to do the things with the combinations but all i get is 20xy?but the answer is 6xy? Can anyone help?

Method 1:

(2x-y)

So the third term

=C

=6xy

Method 2:

You can expand (2x-y)

- #3

Integral

Staff Emeritus

Science Advisor

Gold Member

- 7,201

- 56

x/2 = 3/y is a hyperbola, do a coordinate transform to rotate the coordinate axis by π/2 radians.

you will find that (let u & v be the new axis)

u=xcosθ + ysinθ

v=-xsinθ + ycosθ

Let θ = π/2

solve for x & y

x = (v-u)/sqrt(2) y=(v+u)/sqrt(2)

substituting this back into the origianal relationship gives

(v-u)(v+u)/2 =6

or

v*v - u*u = 12

This is the standard form for a hyperbola.

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