How do you multiply $(x – y^5)^3$ ?

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Answer 1 · 2015-10-04T20:01:18

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

The binomial theorem states that

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

Applying this theorem, we get :

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

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

How do you multiply (x – y^5)^3(x – y^5)^3?