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Expansion of (a^2 - b^2)

If 2x-3y = 10...

Question

If $2 x - 3 y$ = 10 and $x y = 16$ ; find the value of $8 x^{3} - 27 y^{3}$

A

-2880

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B

2880

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C

3880

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D

4880

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Solution

The correct option is C
3880

Given that $2 x - 3 y$ = 10.
Cubing on both sides, we get
$(2 x - 3 y)^{3}$ = $10^{3}$

Using the identity, $(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$

$(2 x - 3 y)^{3}$
$= (2 x)^{3} - (3 y)^{3} - 3 (2 x) (3 y) (2 x - 3 y)$

$\Rightarrow 8 x^{3} - 27 y^{3} - 3 (2 x) (3 y) (2 x - 3 y)$
$= 1000$

Given that $x y = 16$ .

$\Rightarrow$ $8 x^{3} - 27 y^{3} - 18 (16) (10)$ = 1000

$\Rightarrow 8 x^{3} - 27 y^{3} - 2880$ = 1000

$\Rightarrow 8 x^{3} - 27 y^{3}$ = 3880

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8 x^{3} + 27 y^{3} i s e q u a l t o

2 x - 3 y = 10

x y = 16

; find the value of

8 x^{3} - 27 y^{3}

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