The middle term in the expansion of $(x + 4)^{4}$ is:

96 x^{3}

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96 x^{2}

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- 96 x^{2}

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none of the above

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Solution

The correct option is B $96 x^{2}$
Given
$(x + 4)^{4}$
Here the middle terms can be calculated by
middle term $= \frac{n}{2} + 1$

$= \frac{4}{2} + 1$

$= 3^{t h} t e r m$

$=^{4} C_{2} x^{2} 4^{2}$

$= \frac{4!}{2! 2!} x^{2} \times 16$

$= \frac{4 \times 3}{2 \times 1} x^{2} \times 16$

$= 96 x^{2}$

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