Question

(a^2+a)(a-1)-(a-2)(a^2+2a+4)

Answer 1

$(a^{2}+a)(a-1)-(a-2)(a^{2}+2a+4)=(a^{3} -a^{2}+a^{2}-a) - (a^{3} +2a^{2} +4a-2a^{2}-4a-8)= a^{3}-a-a^{3}-2a^{2}-4a+2a^{2} +4a+8=-a+8=8-a.$

Ответ: 8-a

Answer 2

Let's simplify the given expression step by step:

(a^2 + a)(a - 1) - (a - 2)(a^2 + 2a + 4)

Expanding the first term (a^2 + a)(a - 1):

= a^3 - a^2 + a^2 - a = a^3 - a

Expanding the second term (a - 2)(a^2 + 2a + 4):

= a(a^2 + 2a + 4) - 2(a^2 + 2a + 4) = a^3 + 2a^2 + 4a - 2a^2 - 4a - 8 = a^3 - 8

Substituting these results back into the original expression:

(a^3 - a) - (a^3 - 8)

Removing the parentheses:

= a^3 - a - a^3 + 8

Combining like terms:

= -a + 8

Therefore, the simplified expression is -a + 8.