# How do you multiply (x – y^5)^3?

Oct 4, 2015

$= {x}^{3} - 3 {x}^{2} {y}^{5} + 3 x {y}^{10} - {y}^{15}$

#### Explanation:

The binomial theorem states that

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

Applying this theorem, we get :

${\left(x - {y}^{5}\right)}^{3} = {\text{^3C_0x^3+ ""^3C_1x^(3-1)(-y^5)^1+ ""^3C_2x^(3-2)(-y^5)^2 + }}^{3} {C}_{3} {x}^{3 - 3} {\left(- {y}^{5}\right)}^{3}$

$= {x}^{3} - 3 {x}^{2} {y}^{5} + 3 x {y}^{10} - {y}^{15}$