How do you use the binomial series to expand $(2x – 5y)^3$ ?

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Answer 1 · 2016-01-23T12:19:22

$8x^3-30x^2y+150xy^2-125y^3$

$(x+y)^n=sum_(r=0)^n""^nC_rx^(n-r)y^r$ .

So in this particular case we get

$(2x-5y)^3=sum_(r=0)^3""^3Cr(2x)^(3-r)(-5y)^r$

$=""^3C_0(2x)^3+""^3C_1(2x)^2(-5y)+""^3C_2(2x)(-5y)^2+""^3C_3(-5y)^3$

$=8x^3-30x^2y+150xy^2-125y^3$

How do you use the binomial series to expand (2x – 5y)^3 (2x – 5y)^3 ?