Q171 / 270 · NDA 2019 (Phase 1) · Mathematics

What is the number of terms in the expansion of $\left[(2 x-3 y)^2\right.$ $\left.(2 \mathrm{x}+3 \mathrm{y})^2\right]^2 ?$

  • A
    4
  • Correct answer
    B
    5
  • C
    8
  • D
    16

Solution

$\begin{aligned} & \text { } \quad\left[(2 \mathrm{x}-3 \mathrm{y})^2(2 \mathrm{x}+3 \mathrm{y})^2\right]^2 \\ & =\left[\left(4 \mathrm{x}^2-9 \mathrm{y}^2\right)^2\right]^2=\left(4 \mathrm{x}^2-9 \mathrm{y}^2\right)^4 \\ & \therefore \text { Number of terms }=4+1=5\end{aligned}$

Hence, the correct answer is option: 'B'.

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