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The coefficient of x^2 in the expansion of the product (2 - x^2)· ((1 + 2x + 3x^2)^6 + (1 - 4x^2)^6) is |
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Answer» Let a=((1+2x+3x2)6+(1−4x2)6) ∴ Coefficient of x2 in the expansion of the product (2−x)2((1+2x+3x2)6+(1−4x2)6)=2( Coefficient of x2 in a)−1(Constant of expansion) In the expansion of ((1+2x+3x2)6+(1−4x2)6), Constant =1+1=2 Coefficient of x2= Coefficient of x2 in (6C0(1+2x)6(3x2)0)+ Coefficient of x2 in (6C1(1+2x)53)−6C1(4) =6C24+6×3−24 =6=+18−24=54 Then, coefficient of x2 in (2−x)2((1+2x+3x2)6+(1−4x2)6) =2×54−1(2)=108−2=106 |
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