<s>[INST] How does $(x+3)^2 - 2^2$ become $(x+1)(x+5)$? I don't understand how $(x+3)^2 - 2^2$ can be transformed to equal $(x+1)(x+5)$. A short demonstration and/or reference to math rules would be very kind.
 [/INST] Just multiply each part out:
$(x + 3)^{2}$
$= (x + 3)(x + 3)$
$= x^{2} + 3x + 3x + 9$
$= x^{2} + 6x + 9$
Also, $2^{2} = 4$.
So, putting the two above together, we get:
$(x + 3)^{2} - 2^{2}$
$= x^{2} + 6x + 9 - 4$
$= x^{2} + 6x + 5$
And, if you understand how to factor, we get $x^{2} + 6x + 5 = (x + 5)(x + 1)$.
</s>