27x4 + 8xy3 এর উৎপাদক বিশ্লেষণ কোনটি?

A x(3x + 2y)(9x^2 + 6xy + 4y^2)

B x(3x − 2y)(9x^2 − 6xy + 4y^2)

C 3x(9x^3 + 8y^3)

D x(3x + 2y)(9x^2 − 6xy + 4y^2)

Solution

Correct Answer: Option D

27x4 + 8xy3
= x(27x3 + 8y3 )
= x{(3x)3 + (2y)3}
= x(3x + 2y){(3x)2 - 3x.2y + (2y)2}
= x(3x + 2y)(9x2 - 6xy + 4y2 )

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