How do you find the 2nd term in the expansion of #(y-2x)^4#?

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↳Redirected from "How do I change #int_0^1int_0^sqrt(1-x^2)int_sqrt(x^2+y^2)^sqrt(2-x^2-y^2)xydzdydx# to cylindrical or spherical coordinates?"

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Answer 1 · 2016-09-01T18:03:29

#"The reqd. term"=-8y^3x#.

In the Binomial Expansion of #(a+b)^n#, the general #(r+1)^(th)# term,

i.e., #T_(r+1)#, is given by,

#T_(r+1)=""_nC_r*a^(n-r)*b^r#.

In our example, #n=4, a=y, b=-2x, r+1=2, i.e., r=1#

#:. T_(1+1)=T_2=""_4C_1*y^(4-1)*(-2x)^1#

#=4*y^3*(-2x)#

#=-8y^3x#.