The coefficient of x2 in the expansion of 1-x-x210 is A- 10 C2B- 10 C1C- 11 C2D- None of these

The correct option is C (1+x+x^2)^10= ((1 x)(1+x+x^2)/1 x )^10=(1 x^3)^10(1 x)^ 10 Thus, coefficient of x^2 in (1 + x + x^2)^10 = coefficient of x^2 in ( ...

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Byju's Answer

Standard XII

Mathematics

Expansions of the Form (1+x)^(-n) and (1-x)^(-n)

The coefficie...

Question

The coefficient of $x^{2}$ in the expansion of ${1 + x + x^{2}}^{10}$ is

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Solution

The correct option is C
$(1 + x + x^{2})^{10} = {(\frac{(1 - x) (1 + x + x^{2})}{1 - x})}^{1} 0 = (1 - x^{3})^{10} (1 - x)^{- 10} T h u s, c o e f f i c i e n t o f x^{2} i n (1 + x + x^{2})^{10} = c o e f f i c i e n t o f x^{2} i n (1 - x)^{- 10} i . e .,^{10 + 2 - 1} C_{2} =^{11} C_{2}$

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The coefficient of x2 in the expansion of 1+x+x210is

The correct option is C (1+x+x2)10=((1−x)(1+x+x2)1−x)10=(1−x3)10(1−x)−10Thus, coefficient of x2 in (1+x+x2)10=coefficient of x2 in(1−x)−10i.e.,10+2−1C2=11C2

The coefficient of $x^{2}$ in the expansion of ${1 + x + x^{2}}^{10}$ is

The correct option is C
$(1 + x + x^{2})^{10} = {(\frac{(1 - x) (1 + x + x^{2})}{1 - x})}^{1} 0 = (1 - x^{3})^{10} (1 - x)^{- 10} T h u s, c o e f f i c i e n t o f x^{2} i n (1 + x + x^{2})^{10} = c o e f f i c i e n t o f x^{2} i n (1 - x)^{- 10} i . e .,^{10 + 2 - 1} C_{2} =^{11} C_{2}$