Question

How do you multiply `(x + y)^6`?

Answer 1

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

Explanation:

There is no special way to multiply (x+y) with it self six times, but we can use binomial theorem or use Pascal's triangle to write the result.

`(x+y)^6 = x^6 +6/1x^5 y +(6*5)/(2*1) x^4y^2 +(6*5*4)/(3*2*1) x^3y^3 + (6*5*4*3)/(4*3*2*1) x^2y^4 + (6*5*4*3*2)/(5*4*3*2*1) x y^5 + (6*5*4*3*2*1)/(6*5*4*3*2*1) y^6`

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