Question:
The constant term in the expansion of $(2x^{2}-\frac{1}{x^{2}})^{6}$ is ________.
The constant term in the expansion of $(2x^{2}-\frac{1}{x^{2}})^{6}$ is ________.
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Constant term means the $x^0$ term.
Updated On: Jun 26, 2026
- -160
- 160
- -180
- 180
- 0
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Constant term is the term independent of $x$ (power of $x$ is 0).
Step 2: Meaning
$T_{r+1} = ^6C_r (2x^2)^{6-r} (-x^{-2})^r = ^6C_r 2^{6-r} (-1)^r x^{12-2r-2r}$.
Step 3: Analysis
Set $12-4r = 0 \implies r = 3$. $T_4 = ^6C_3 2^{6-3} (-1)^3 = 20 \times 8 \times (-1) = -160$.
Step 4: Conclusion
The constant term is -160. Final Answer: (A)
Constant term is the term independent of $x$ (power of $x$ is 0).
Step 2: Meaning
$T_{r+1} = ^6C_r (2x^2)^{6-r} (-x^{-2})^r = ^6C_r 2^{6-r} (-1)^r x^{12-2r-2r}$.
Step 3: Analysis
Set $12-4r = 0 \implies r = 3$. $T_4 = ^6C_3 2^{6-3} (-1)^3 = 20 \times 8 \times (-1) = -160$.
Step 4: Conclusion
The constant term is -160. Final Answer: (A)
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