Which of the following is the factor of the given polynomial ?

$8 x^{3} + 27 y^{3} + 36 x^{2} y + 54 x y^{2}$

(2 x - 3 y)^{2}

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(2 x + 3 y)^{3}

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(x - 3 y)^{3}

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(x - y)^{3}

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Solution

The correct option is B
$(2 x + 3 y)^{3}$
The given polynomial $(2 x)^{3} + (3 y)^{3} + 18 x y (2 x + 3 y)$ can be written as

$= (2 x)^{3} + (3 y)^{3} + 3 (2 x) (3 y) (2 x + 3 y) = (2 x + 3 y)^{3}$
Hence, the correct answer is option (b)

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Similar questions

8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3}

8 x^{3} + 36 x^{2} y + 54 x y^{2} + 27 y^{3} .

The value of $(2 x + 3 y)^{3}$ is __________.

8 x^{3} + 27 y^{3} + 36 x^{3} y + 54 x y^{2}

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