expand (x-y)^7?

Question

This is on a bonus quiz. There could be a trick to it.

Answer 1

X^7 - 7X^6*Y + 21X^5*Y^2 - 35X^4*Y^3 + 35X^3*Y^4 -21X^2*Y^5 + 7X*Y^6 - Y^7

The coefficients go like this:
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

Answer 2

X^7 - 7X^6*Y + 21X^5*Y^2 - 35X^4*Y^3 + 35X^3*Y^4 -21X^2*Y^5 + 7X*Y^6 - Y^7

use pascale triangule to find coefficient
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1

Answer 3

No trick... just binomial expansion is all.

x^7 - 7x^6·y + 21x^5·y² - 35x^4·y³ + 35x³·y^4 - 21x²·y^5 + 7x·y^6 - y^7

If you like, it's
∑ C(7, k) · x^(7 - k) · y^k,
for k going from 0 to 7. Pascal's triangle is helpful with the combinations.

Answer 4

x^7 - 7·y·x^6 + 21·y^2·x^5 - 35·y^3·x^4 + 35·y^4·x^3 - 21·y^5·x^2 + 7·y^6·x - y^7

Answer 5

using binomial expansion
(x-y)^7 = x^7-7x^6y+21x^5y^2 - 35x^4y^3+35x^3y^4-21x^2y^5+ 7xy^6- y*7

starting from 0 nth term is Cn x^(7-n) (-1y)^n

Cn = n thngs taken from 7 at a time = 7!/(n!(7-n)!)

Answer 6

(x - y)^7 = x^7 - 7x^6y + 21x^5y^2 - 35x^4y^3 + 35x^3y^4 - 21x^2y^5 + 7xy^6 - y^7

Answer 7

Use FOIL (First interior outdoors final) First do (x instances x) then (x instances 5y) then (y instances x) then (y instances 5y) positioned all of it jointly to get x^2 + 5xy +xy +5y^2 combine like words to get: x^2 + 5y^2 +6xy desire this helps!!

Answer 8

the only trick is that you have to FOIL it out. (first outside inside last).

But im sure you know how to do that!

Its NOT x^7-y^7.

It's the result of (x-y)(x-y)(x-y)(x-y)(x-y)(x-y)(x-y)

Answer 9

x^7 -C(7,1)x^6y + C(7,2)x^5y^2 - C(7,3)x^4y^3 + C(7,4)x^3y^4 - C(7,5)x^2y^5 + C(7,6)xy^6 - y^7

C(7,n) = 7!/[n!(7-n))!]