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?
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, $-4 \pm \sqrt 6$