!9. Simplify $\frac{b x\left(a^{2} x^{2}+2 a^{2} y^{2}+b^{2} y^{2}\right)}{b x+a y}$
$$
+\frac{a y\left(a^{2} x^{2}+2 b^{2} x^{2}+b^{2} y^{2}\right)}{b x+a y}
$$
(A) $a^{2} x^{2}+b^{2} y^{2}$.(B) $(a x+b y)^{2}$.
(C) $(a x+b y)(b x+a y)$. (D) $2\left(a^{2} x^{2}+b^{2} y^{2}\right)$.
(E) $(b x+a y)^{2}$.
19
B
19. The hint from the options suggests that the numerator can be divisible by $b x + a y$. For this, the original expression in the numerator can be transformed as follows:
$$
\begin{aligned}
& b x\left(a^{2} x^{2}+b^{2} y^{2}\right)+a y\left(a^{2} x^{2}+b^{2} y^{2}\right) \\
+ & b x\left(2 a^{2} y^{2}\right)+a y\left(2 b^{2} x^{2}\right) \\
= & (b x+a y)\left(a^{2} x^{2}+b^{2} y^{2}\right)+2 a b x y(a y+b x) \\
= & (b x+a y)(a x+b y)^{2} .
\end{aligned}
$$