Find the Value
\[ 3x-2y=11 \]
\[ xy=12 \]
Find:
\[ 27x^3-8y^3 \]
Solution:
Using identity:
\[ a^3-b^3=(a-b)^3+3ab(a-b) \]
Here,
\[ a=3x,\quad b=2y \]
\[ a-b=11 \]
\[ ab=(3x)(2y)=6xy=6(12)=72 \]
\[ 27x^3-8y^3 = (11)^3+3(72)(11) \]
\[ = 1331+2376 \]
\[ =3707 \]