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# Find the value of ${{\text{x}}^{\text{3}}}{\text{ - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36xy - 216,}}$ when ${\text{x = 2y + 6}}$  Verified
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Hint: As per the given polynomial, and the condition given, we just need to replace the given condition into ${{\text{x}}^{\text{3}}}{\text{-8}}{{\text{y}}^{\text{3}}}{\text{ - 36xy - 216,}}$ this meansl means directly replace the value of x in the given polynomial and solve to get the required answer.

The given polynomial is ${{\text{x}}^{\text{3}}}{\text{ - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36xy - 216,}}$and the condition is ${\text{x = 2y + 6}}$
$\Rightarrow {{\text{x}}^{\text{3}}}{\text{ - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36xy - 216}} \\ {\text{as,x = 2y + 6}} \\ \Rightarrow {\text{(2y + 6}}{{\text{)}}^{\text{3}}}{\text{ - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36(2y + 6)y - 216}} \\$
Now, using the formula of ${{\text{(a + b)}}^{\text{3}}}{\text{ = }}{{\text{a}}^{\text{3}}}{\text{ + }}{{\text{b}}^{\text{3}}}{\text{ + 3ab(a + b)}}$and simplifying the equation further,
${\text{ = (2y}}{{\text{)}}^{\text{3}}}{\text{ + (6}}{{\text{)}}^{\text{3}}}{\text{ + 3(2y)(6)(2y + 6) - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36(2y + 6)y - 216}} \\ {\text{ = 8}}{{\text{y}}^{\text{3}}}{\text{ + 216 + 36(2y + 6)y - 8}}{{\text{y}}^{\text{3}}}{\text{ - 36(2y + 6)y - 216}} \\ {\text{ = 0}} \\$