Question

Coefficient of x ^2 in the expansion of (x-2)^3

Answer 1

Given Expansion -

=> ( x - 2 )³

$\sf{ ^n C_0 x^3 y ^ 0 + ^n C_1 x^2 y + ^n C_2 x y ^ 2 + ^n C n x ^ 0 y ^ 3 } \\ \\ \sf{ \implies { x^3 + 3x^2 y + 3 x y ^ 2 + y ^ 3}} \\ \\ \sf{ \implies { x ^ 2 ( x + 3y ) + 3 x y ^2 + y ^ 3 }}$

So , we can say that , the coefficent of x² in the expansion of ( x - 2 )³ is ( x + 3 y ) .

This is the required answer .

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AddiTiOnaL InFoRmAtIon -

$\sf{ ( x + y ) ^ n = \: ^n C_0 x^n y ^ 0 + ^n C_1 x^(n - 1) y + ^n C_2 x ^ ( n - 2 ) y ^ 2 + ....... + ^n C n x ^ 0 y ^ n }$

$\sf{ ( x - y ) ^ n = \: ^n C_0 x^n y ^ 0 - ^n C_1 x^(n - 1) y + ^n C_2 x ^ ( n - 2 ) y ^ 2 - ....... + ^n C n x ^ 0 y ^ n }$