Find the Product:
\[ (3x + 2y + 2z) \] \[ (9x^2 + 4y^2 + 4z^2 – 6xy – 4yz – 6zx) \]
Solution:
Using identity:
\[ (a+b+c)(a^2+b^2+c^2-ab-bc-ca) = a^3+b^3+c^3-3abc \]
Here, \[ a=3x,\qquad b=2y,\qquad c=2z \]
\[ (3x + 2y + 2z) \] \[ (9x^2 + 4y^2 + 4z^2 – 6xy – 4yz – 6zx) \]
\[ = (3x)^3+(2y)^3+(2z)^3 -3(3x)(2y)(2z) \]
\[ = 27x^3+8y^3+8z^3-36xyz \]