Transform the following expression into a perfect square:

$$
9 a^{4} b^{2}-42 a^{2} b
$$
$\left(-42 a^{2} b\right)$ includes the double product of the first and second term of the binomial, and since the first term of the binomial is $3 a^{2} b$, the second term is:

$$
-42 a^{2} b: 6 a^{2} b=-7
$$

thus

$$
9 a^{4} b^{2}-42 a^{2} b+(-7)^{2}=\left(3 a^{2} b-7\right)^{2}
$$

(Zoltán Harsányi, Eger.)