if in the expansion of ( 1+x)^ m (1 -x) ^n, the coefficients of x and x^2 are 3 and -6 then n=?

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Please find below the solution to the asked query:

We have1+xm 1-xn=1+mC1x+mC2x2+mC3x3+...... 1-nC1x+nC2x2-nC3x3+......Cofficient of x will be obtained  when constant term in first bracket is multipliedwith the term having x in second bracket.Given that coefficient of x =3mC1-nC1=3m-n=3m=n+3x2 will be obtained by:x2×ConstantConstant×x2x×xCoefficient of x2 =-6mC2+nC2-mC1.nC1=-6mm-12+nn-12-mn=-6n+3n+3-12+nn-12-n+3n=-6n+3n+2+nn-1-2n+3n=-12n2+5n+6+n2-n-2n2-6n+12=02n2-2n2-2n+18=02n=18n=9

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