Strange maths coincidence $(6\times 9)+(6+9)=69?$

Question

Is this a freak coincidence in maths or there are more of this type of maths calculation?

$$\color{red}{(6\times 9)}+\color{blue}{(6+9)}=69$$

I try to find more, but I can't. Can you?

Answer 1

You can simply rewrite it as:

$$ab+a+b=10a+b$$ $$ab=9a$$

One can see now, that $b=9$ and $a$ can be anynumber such that $0 \leq a \leq 9$.

Answer 2

For base $r,$

$$ab+a+b=ra+b\iff b=r-1$$ for $a\ne0$

Answer 3

$$(6 \times 9) + (6 + 9) = 10 \times 6 + 9 = 69$$

Similarly, $$(n \times 9) + (n + 9) = 10 \times n + 9 = \text{"}n9\text{''},$$ for any one-digit number $n$