<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] Yet another way of looking at it is to look at the roots.
$(x+3)^2-2^2=0$, so $(x+3)^2=2^2$.   Taking square roots, we get $x+3=2$ or $x+3=-2$.   Solving for x, we get $x=-1$ or $x=-5$.   That means the quadratic is of the form $a(x+1)(x+5)$ where $a$ is the coefficient of your $x^2$ term, which in this case is 1.
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