Coefficient of x^3 in the expansion of (x^2 - | vedclass

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Question

$\left(x^{2}-x+1\right)^{10} \cdot\left(x^{2}+\right)^{15}$

$=\left(1+^{10} \mathrm{C}_{1}\left(\mathrm{x}^{2}-\mathrm{x}\right)+^{10} \mathrm{C}_{

Vedclass · Accepted Answer

$-360$

Vedclass · Answer

$\left(x^{2}-x+1\right)^{10} \cdot\left(x^{2}+\right)^{15}$

$=\left(1+^{10} \mathrm{C}_{1}\left(\mathrm{x}^{2}-\mathrm{x}\right)+^{10} \mathrm{C}_{2}\left(\mathrm{x}^{2}-\mathrm{x}\right)^{2}+^{10} \mathrm{C}_{3}\left(\mathrm{x}^{2}-\mathrm{x}\right)^{3}\right)$

$\left(^{15} \mathrm{C}_{0}+^{15} \mathrm{C}_{1}, \mathrm{x}^{2}\right)$

$=-2 \cdot^{10} \mathrm{C}_{2} \cdot^{15} \mathrm{C}_{0}-^{10} \mathrm{C}_{1} \cdot^{15} \mathrm{C}_{1}-^{10} \mathrm{C}_{3}=-360$

Coefficient of $x^3$ in the expansion of $(x^2 - x + 1)^{10} (x^2 + 1 )^{15}$ is equal to

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