Question : What is the value of $(27 x^{3} - 58 x^{2} y + 31 x y^{2} - 8 y^{3})$ , when $x = - 5$ and $y = - 7 ?$
Option 1: 1924
Option 2: – 1924
Option 3: – 1926
Option 4: 1926

Question

Question : What is the value of $(27 x^{3} + 58 x^{2} y + 31 x y^{2} + 8 y^{3})$ , when $x = 5$ and $y = - 7$ ?

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Answer 1

Correct Answer: 1924

Solution : Given:
$x = - 5$ and $y = - 7$
$(27 x^{3} - 58 x^{2} y + 31 x y^{2} - 8 y^{3})$
$= (3 x)^{3} - 3 \times (3 x)^{2} \times 2 y + 3 \times 3 x \times (2 y)^{2} - (2 y)^{3} - 4 x^{2} y - 5 x y^{2}$
$= (3 x - 2 y)^{3} - x y (4 x + 5 y)$
$= (3 \times (- 5) - 2 \times (- 7))^{3} - (- 5 \times (- 7)) (4 \times (- 5) + 5 \times (- 7))$
$= - 1 - 35 (- 20 - 35)$
$= - 1 - 35 (- 55)$
$= - 1 + 1925$
$= 1924$
Hence, the correct answer is 1924.

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Question : What is the value of (27x3−58x2y+31xy2−8y3), when x=−5 and y=−7?Option 1: 1924Option 2: – 1924Option 3: – 1926Option 4: 1926

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Question : What is the value of $(27 x^{3} - 58 x^{2} y + 31 x y^{2} - 8 y^{3})$ , when $x = - 5$ and $y = - 7 ?$
Option 1: 1924
Option 2: – 1924
Option 3: – 1926
Option 4: 1926