Question

Using Pascal’s triangle, determine the first four terms of the expanded expression (x + y)4.

Answer 1

x^4+ 4x^3y+6x^2y^2+4xy^3+y4

Answer 2

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

Explanation:

Given is an algebraic expression raised to power 4

`(x+y)^4\\`

Let us write 4 rows of Pascal triangle

1

1 2 1

1 3 3 1

1 4 6 4 1

Thus we find coefficients as 1,4,6,4,1 and x will be having reduced powers while y will have increasing powers.

Hence expansion would be

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