Multiply : \( (x^2 + 4y^2 + 2xy – 3x + 6y + 9) \) by \( (x – 2y + 3) \)
\[
(x^2 + 4y^2 + 2xy – 3x + 6y + 9)(x – 2y + 3)
\]
\[
= x^3 – 2x^2y + 3x^2
+ 4xy^2 – 8y^3 + 12y^2
+ 2x^2y – 4xy^2 + 6xy
\]
\[
\quad – 3x^2 + 6xy – 9x
+ 6xy – 12y^2 + 18y
+ 9x – 18y + 27
\]
\[
= x^3 – 8y^3 + 18xy + 27
\]