how to i expand (X + Y)^4?

Answer 1

(X+Y)^n = ∑ C(n,r)*X^r * Y^(n-r)

(X+Y)^4 = X^4 + 4X^3Y + 6x^2Y^2 + 4Xy^3 + Y^4

If you know about Pascal's triangle you could also have just substituted the coefficients.

Answer 2

use the 4th row of Pascal's triangle (1, 4, 6, 4, 1) and expand the binomial with the binomial theorem:

1x^4 + 4x^3y + 6x²y² + 4xy^3 + y^4

Answer 3

First, you are going to get something that looks like

ax^4 + bx^3y + cx^2y^2 + dx^y3 + ey^4

Using Pascal's triangle, we can find the values of a through e

1
1 . 1
1 . 2 . 1
1 . 3 . 3 . 1
1 . 4 . 6 . 4 . 1

So

x^4 + 4x^3y + 6x^2y^2 + 4x^y3 + y^4

Answer 4

Either manually using FOIL, or using Binomial expansion:

(x+y)^4 = x^4 + 4x^3y + 6x^2y^2 + 4xy^3 + y^4

Answer 5

Use Pascal's triangle
1
11
121
1331
14641

The x exponents go down, the y go up

x^4+4x^3y+6x^2y^2+4xy^3+y^4

Answer 6

can be done effectively using binomial theorem, or as simple by
(X+Y)^4= ((X+Y)^2) *((X+Y)^2)