Question

Find the middle terms in the expansion of ${(2x^2-\frac{1}{x})}^7$

• A. $-560x^5,280x^2$
• B. $-280x^5,560x^2$
• C. $560x^5,-280x^2$
• D. $280x^5,-560x^2$

Answer 1

The correct option is A $-560x^5,280x^2$

The middle terms will be $T_4$ and $T_5$
Now, $T_4$
$=T_{3+1}$
$=-{}^7{C}_3{.2}^4.x^{8-3}$
$=-35.\left(16\right).x^5$
$=-560.x^5$
$T_5$
$=T_{4+1}$
$={}^7{C}_4{.2}^3.x^{6-4}$
$=35.\left(8\right).x^2$
$=280.x^2$