Coefficients of a power

#coefficient#expansion#binomial

Statement

Find the coefficient of $x^4$ in $(2+x)^7$ .

Hint

$\binom{7}{4}2^{7-4}$ .

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Term of degree 4. $\binom{7}{4}2^{7-4}x^4=\binom{7}{4}\cdot 8x^4=35\cdot 8=280$ .

Conclusion. The coefficient is $280$ .