8-3. What will be the result if we expand and combine like terms in the expression $(a+1)(a+3)(a+4)(a+5)(a+6)$?

a) $a^{5}+360$.

b) $a^{5}+19 a^{4}+137 a^{3}+461 a^{2}+702 a+360$

c) $a^{5}+19 a^{4}+138 a^{3}+476 a^{2}+776 a+480$.

d) $a^{4}+18 a^{3}+119 a^{2}+342 a+360$.

e) $a^{5}+18 a^{4}+123 a^{3}+402 a^{2}+656 a+480$.
Answer: b).

Solution. We will discard all options except b):

- option a) is incorrect because, in addition to the two terms mentioned, there should be some others;
- option d) is incorrect, as it resulted in a polynomial of the 4th degree;
- options c) and e) are incorrect, as they have the wrong constant term.