Question

What is the correct expansion of the binomial (x + y)5?
x5 + 5x4y + 10x3y2 + 10x3y3 + 5xy4 + y5
x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y4
x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + y5
x5 + 5x4y4 + 10x3y3 + 10x2y2 + 5xy + y5

Answer 1

The coefficients are all identical and correct, so nothing to check there.
hint:
Example for expansion of (1+x)^6:
\(y^6+6xy^5+15x^2y^4+20x^3y^3+15x^4y^2+6x^5*y+x^6\)
Note the progression of \(powers\) of each term.