<s>[INST] Why is $(5\sqrt{5p}-3\sqrt{5q})(5\sqrt{5p}+3\sqrt{5q}) \equiv 5(5p-3q)(5p+3q)$? I was working on the difference of two squares, $125p^2-45q^2$ 
Writing my answer, $$(5\sqrt{5}p-3\sqrt{5}q)(5\sqrt{5}p+3\sqrt{5}q),$$ onto Pearson, I got a popup that said my answer was equivalent to the correct answer but in incorrect form. Apparently, the correct answer is $$5(5p-3q)(5p+3q).$$
Why is that? I'm failing to see the intuition here.
 [/INST] $$125p^2-45q^2=5(25p^2-9q^2)=5(5p+3q)(5p-3q)$$
Your answer was incorrect because it should have been
$$125p^2-45q^2=(\sqrt{125}p^2+\sqrt{45}q^2)(\sqrt{125}p^2-\sqrt{45}q^2)=(5\sqrt{5}p+3\sqrt{5}q)(5\sqrt{5}p-3\sqrt{5}q)=5(5p+3q)(5p-3q)$$
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