Find the Product:
\[ (3x + 2y)(9x^2 – 6xy + 4y^2) \]
Solution:
Using identity:
\[ (a+b)(a^2-ab+b^2)=a^3+b^3 \]
Here, \[ a=3x,\qquad b=2y \]
\[ (3x + 2y)(9x^2 – 6xy + 4y^2) \]
\[ = (3x + 2y)\left[(3x)^2 – (3x)(2y) + (2y)^2\right] \]
\[ = (3x)^3 + (2y)^3 \]
\[ = 27x^3 + 8y^3 \]