Question

(a+1)(a+2)(a²+4)(a²+1)(a-2)(a-1)​

Answer 1

Ответ:

Решение в приложении.

Объяснение:

Answer 2

To simplify the expression $(a+1)(a+2)(a^2+4)(a^2+1)(a-2)(a-1)$, you can use the distributive property and then simplify further by combining like terms:

1. Start with the expression: $(a+1)(a+2)(a^2+4)(a^2+1)(a-2)(a-1)$

2. Expand the first two terms $(a+1)(a+2)$ using the distributive property: $(a^2+2a+a+2)(a^2+4)(a^2+1)(a-2)(a-1)$

3. Combine like terms in the first set of parentheses: $(a^2+3a+2)(a^2+4)(a^2+1)(a-2)(a-1)$

4. Expand the next two terms $(a^2+3a+2)(a^2+4)$ using the distributive property: $(a^4+4a^2+3a^3+12a^2+2a^2+8a+3a+12)(a^2+1)(a-2)(a-1)$

5. Combine like terms in the expanded expression: $(a^4+3a^3+18a^2+11a+12)(a^2+1)(a-2)(a-1)$

6. Expand the next term $(a^2+1)(a-2)$ using the distributive property: $(a^4+3a^3+18a^2+11a+12)(a^3-a^2-2a-2)$

7. Finally, expand the last term $(a^3-a^2-2a-2)(a-1)$ using the distributive property:

   $$a^4+3a^3+18a^2+11a+12 = \boxed{a^7 - a^6 - 2a^5 + a^4 - 3a^3 + 3a^2 - 9a + 12}$$

So, the simplified expression is $a^7 - a^6 - 2a^5 + a^4 - 3a^3 + 3a^2 - 9a + 12$.