Find the value of $x^{3} + 27 y^{3} + 9 x^{2} y + 27 x y^{2}$ when $x = 55$ and $y = 15$ .

772544

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1000000

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100000000

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778342

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Solution

The correct option is B
1000000

The given expression is similiar to the expansion of the identity $(a + b)^{3}$ , i.e.,

$x^{3} + 27 y^{3} + 9 x^{2} y + 27 x y^{2} = x^{3} + (3 y)^{3} + 3 \times x^{2} \times 3 y + 3 \times x \times (3 y)^{2} = (x + 3 y)^{3}$

Substituting the values of $x$ and $y$ in $(x + 3 y)^{3}$

$\Rightarrow (x + 3 y)^{3} = (55 + 3 \times 15)^{3} = 100^{3} = 1000000$

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