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What's the coefficient of $x^7$ in $(2x+4)^{10}$?
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Given that $(2x+4)^{10}$

Directly we can apply the Binomial theorem
$(a+b)^{n}=\sum_{k=0}^{n}\binom{n}{k}(a)^{n-k}\cdot(b)^{k}$

Now$,(2x+4)^{10} =\sum_{k=0}^{10}\binom{10}{k}(2x)^{10-k}\cdot(4)^{k}$

We want coefficient of $x^{7},$so we can put $k=3$ and we get $x^{7},$

$\Rightarrow\binom{10}{3}(2x)^{10-3}\cdot(4)^{3}$

$\Rightarrow\binom{10}{3}(2x)^{7}\cdot(4)^{3}$

$\Rightarrow\binom{10}{3}(2)^{7}\cdot x^{7}\cdot(4)^{3}$

So,Coefficient of $x^{7}$ is $:\binom{10}{3}(2)^{7}\cdot(4)^{3}$

                                         $\Rightarrow120\cdot128\cdot64$

                                          $\Rightarrow983,040$

So,correct answer is$:983,040$

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