Question

How do you multiply `(x – y^5)^3`?

Answer 1

`=x^3-3x^2y^5+3xy^10-y^15`

Explanation:

The binomial theorem states that

`(x+y)^n=sum_(r=1)^n ""^nC_rx^(n-r)y^r`

Applying this theorem, we get :

`(x-y^5)^3= ""^3C_0x^3+ ""^3C_1x^(3-1)(-y^5)^1+ ""^3C_2x^(3-2)(-y^5)^2 + ""^3C_3x^(3-3)(-y^5)^3`

`=x^3-3x^2y^5+3xy^10-y^15`