If $2 x + 3 y = 12$ and $x y = 6$ , find the value of $8 x^{3} + 27 y^{3}$ .

Question

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Answer 1

$2 x + 3 y = 12$ $x y = 6$
$8 x^{3} + 27 y^{3}$
$= (2 x)^{3} + (3 y)^{3}$
$= a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$8 x^{3} + 27 y^{3} = (2 x + 3 y) ((2 x)^{2} + (3 y)^{2} - (2 x) (3 y))$
$= (12) [(2 + 3 y)^{2} - 12 x y - 6 x y]$
$= (12) [(12)^{2} - 18 (6)]$
$= 12 [144 - 108]$
$= 12 \times 36$
$= 432$ .

Answer 2

2 x + 3 y = 12

x y = 6

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

= (2 x)^{3} + (3 y)^{3}

= a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)

8 x^{3} + 27 y^{3} = (2 x + 3 y) ((2 x)^{2} + (3 y)^{2} - (2 x) (3 y))

= (12) [(2 + 3 y)^{2} - 12 x y - 6 x y]

= (12) [(12)^{2} - 18 (6)]

= 12 [144 - 108]

= 12 \times 36

= 432

.