Question

If x-2y=3 then what is the value of x³-8y³-18xy?​

Answer 1

$\huge\mathbb{SOLUTION:-}$

• We have to find the value of

• $\sf x{}^{3}-8y{}^{3}-18xy$

Now :-

$\bf\underline{\underline{Step\:by\:step\: Explanation:-}}$

• Identity used :-

$\sf (a-b){}^{3}=a{}^{3}-b{}^{3}-3ab(a-b)$

• Given the value of x-2y=3

$\sf\implies (x-2y){}^{3}=x{}^{3}-(2y){}^{3}-3\times x\times 2y(x-2y)\\ \\ \sf\implies (3){}^{3}=x{}^{3}-8y{}^{3}-6xy(3)\\ \\ \sf\implies 9=x{}^{3}-8y{}^{3}-18xy$

• The value of this expression is 9

$\underline{\boxed{\sf{\purple{x{}^{3}-8y{}^{3}-18xy=9}}}}$