Q175 / 270 · NDA 2023 (Phase 1) · Mathematics

How many terms are there in the expansion of $(3 x-y)^4(x+3 y)^4$ ?

  • A
    $9$
  • B
    $12$
  • Correct answer
    C
    $15$
  • D
    $17$

Solution

$(3 x-y)^4(x+3 y)^4$ $=[(3 x-y)(x+3 y)]^4=\left(3 x^2+8 x y-3 y^2\right)^4$ Number of terms $={ }^{4+3-1} C_{3-1}={ }^6 C_2=15$.

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

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