Question

Find the middle term(s) in the expansion of:
$\rm \Big(x^{2} - \frac{2}{x} \Big)^{8}$

Answer 1

Answer:

middle term(s) in the expansion =  1120 x⁴

Step-by-step explanation:

(x²   - 2/x)⁸

there will be total 9 terms

middle term would be 5 th term

5th Term would be

⁸C₅₋₁ (x²)⁸⁺¹⁻⁵(-2/x)⁵⁻¹

= ⁸C₄(x²)⁴(-2/x)⁴

={ 8*7*6*5/(4 * 3* 2 * 1) }  x⁸ * 16 /x⁴

= 70 * x⁴ * 16

= 1120 x⁴

middle term(s) in the expansion =  1120 x⁴

Answer 2

Answer:

1120 x⁴

Step-by-step explanation:

In this question,

We have to find the middle term

$(x^{2}\ -\ \frac{2}{x})^{8}$

According to the question,

There will be total of 9 terms

Middle term would be the 5th term

Therefore,5th Term would be

$^{8}C_{5-1} (x^{2})^{8+1-5}(\frac{-2}{x})^{5-1}$

= $^{8}C_{4}(x^{2})^{4}(\frac{-2}{x})^{4}$

= $\frac{8\times 7\times 6\times 5}{4\times 3\times 2\times 1}$$\frac{x^{8}\times 16}{\times x^{4}}$

= $70\times x^{4}\times 16$

= 1120 x⁴

Middle term(s) in the expansion =  1120 x⁴