The coefficient of x^{4} is the expansion of | vedclass

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Question

$\left(1+x+x^{2}\right)^{10}$

$=^{10} \mathrm{C}_{0}+^{10} \mathrm{C}_{1} \mathrm{x}(1+\mathrm{x})+^{10} \mathrm{C}_{2} \mathrm{x}^{2}(1+\mathrm{x}

Vedclass · Accepted Answer

$615$

Vedclass · Answer

$\left(1+x+x^{2}ight)^{10}$

$=^{10} \mathrm{C}_{0}+^{10} \mathrm{C}_{1} \mathrm{x}(1+\mathrm{x})+^{10} \mathrm{C}_{2} \mathrm{x}^{2}(1+\mathrm{x})^{2}$

$+^{10} \mathrm{C}_{3} \mathrm{x}^{3}(1+\mathrm{x})^{3}+^{10} \mathrm{C}_{4} \mathrm{x}^{4}(1+\mathrm{x})^{4}+\ldots \ldots$

Coeff. of $\mathrm{x}^{4}=^{10} \mathrm{C}_{2}+^{10} \mathrm{C}_{3} 	imes^{3} \mathrm{C}_{1}+^{10} \mathrm{C}_{4}=615$

The coefficient of $x^{4}$ is the expansion of $\left(1+\mathrm{x}+\mathrm{x}^{2}\right)^{10}$ is

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