<s>[INST] Algebra precalculus factorization I must factor this out:$(a+1)(a+3)(a+5)(a+7)+15$
I know that it might have an artifice or technique to transform those factors, but i cannot find any idea on how to do it. 
PS.The majority of my questions are about factoring polynomials. Is there an app or site on internet where I can see step by step the resolution of these exercices so then I won't bother you guys anymore with a lot of these kind of silly questions?
 [/INST] take $$ b = a+4  $$
$$ (b-3)(b-1)(b+1)(b+3) + 15 $$
$$ (b-1)(b+1)(b-3)(b+3) + 15 $$
$$ (b^2-1)(b^2-9) + 15 $$
$$  b^4 - 10 b^2 + 9 + 15  $$
$$  b^4 - 10 b^2 + 24  $$
take $u = b^2$
$$ u^2 - 10 u + 24 $$
$$  (u - 4)(u - 6)  $$
$$  (b^2 - 4)(b^2 - 6)  $$
$$  (a^2 + 8 a + 16 - 4) (a^2 + 8 a + 16 - 6) $$
$$  (a^2 + 8 a + 12) (a^2 + 8 a + 10) $$
$$  (a + 6)(a+2) (a^2 + 8 a + 10) $$
The roots of $a^2 + 8 a + 10$ are real numbers but not rational, $-4 \pm \sqrt 6$
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