Find the Value
\[ 3x+2y=14 \]
\[ xy=8 \]
Find:
\[ 27x^3+8y^3 \]
Solution:
Using identity:
\[ a^3+b^3=(a+b)^3-3ab(a+b) \]
Here,
\[ a=3x,\quad b=2y \]
\[ a+b=14 \]
\[ ab=(3x)(2y)=6xy=6(8)=48 \]
\[ 27x^3+8y^3 = (14)^3-3(48)(14) \]
\[ = 2744-2016 \]
\[ =728 \]