If x = 2y + 6,then what is the value of x^3 - | vedclass

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(B) Given the equation $x = 2y + 6$,we can rewrite it as $x - 2y = 6$.To find the value of $x^3 - 8y^3 - 36xy - 216$,we can express it as $x^3 + (-2y)

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(B) Given the equation $x = 2y + 6$,we can rewrite it as $x - 2y = 6$.To find the value of $x^3 - 8y^3 - 36xy - 216$,we can express it as $x^3 + (-2y)^3 + (-6)^3 - 3(x)(-2y)(-6)$.Recall the algebraic identity: $a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)$.Alternatively,consider the identity $(a + b + c)^3 = a^3 + b^3 + c^3 + 3(a + b)(b + c)(c + a)$.Let $a = x$,$b = -2y$,and $c = -6$.Then $a + b + c = x - 2y - 6$. Since $x - 2y = 6$,we have $a + b + c = 6 - 6 = 0$.If $a + b + c = 0$,then $a^3 + b^3 + c^3 = 3abc$.Substituting the values: $x^3 + (-2y)^3 + (-6)^3 = 3(x)(-2y)(-6)$.$x^3 - 8y^3 - 216 = 36xy$.Rearranging the terms: $x^3 - 8y^3 - 36xy - 216 = 0$.

If $x = 2y + 6$,then what is the value of $x^3 - 8y^3 - 36xy - 216$?

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