If $3x – 2y= 11$ and $xy = 12$, find the value of $27x^3 – 8y^3$.

Given:

$3x – 2y= 11$ and $xy = 12$

To do:

We have to find the value of $27x^3 - 8y^3$.

Solution:

We know that,

$(a-b)^3=a^3 - b^3 - 3ab(a-b)$

Therefore,

$3x - 2y = 11$

Cubing both sides, we get,

$(3x – 2y)^3 = (11)^3$

$(3x)^3 – (2y)^3 – 3 \times 3x \times 2y(3x – 2y) =1331$

$27x^3 – 8y^3 – 18xy(3x -2y) =1331$

$27x^3 – 8y^3 – 18 \times 12 \times 11 = 1331$

$27x^3 – 8y^3 – 2376 = 1331$

$27x^3 – 8y^3 = 1331 + 2376$

$27x^3 – 8y^3 = 3707$

The value of \( 27x^{3}-8y^3 \) is $3707$.   

Tutorialspoint

Updated on: 10-Oct-2022

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