Question

Which of the following is the correct expansion of the binomial (x + y)6?

Answer 1

Hello,

Pascal Triangle:
1
1 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

x^6+6x^5y+15 x^4y² +20 x^3y^3 + 15 x²y^4+6 x y^5 +y^6

Answer 2

x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6

Explanation:

expansion of the binomial (x + y)^6

USe Pascals triangle

6th row in pascals triangle is

1 6 15 20 15 6 1

Now we do the expansion using the above row.

nCr (x)^n-r (y)^r

1 (x)^6(y)^0+ 6(x)5(y)^1+ 15(x)^4(y)^2+20(x)^3(y)^3+15(x)^2(y)^4+6(x)^1(y)^5+1(x)^0(y)^6

`x^6+6x^5y+15x^4y^2+20x^3y^3+15x^2y^4+6xy^5+y^6`