Question

2(a+1)(a^2+1)-(a-1)(a^2+1)-(a+3)(a^2-1) (n-1)(n-2)-(n+3)(n-2)+(n+3)(n+2)

Answer 1

Советую приложение photomath оно легко решает такие примеры, объясняя все этапы действий

Answer 2

Let's simplify each expression step by step:

1. Simplifying 2(a+1)(a^2+1): Distribute 2 across the terms: 2(a+1)(a^2+1) = 2a(a^2+1) + 2(a^2+1) = 2a^3 + 2a + 2a^2 + 2

2. Simplifying (a-1)(a^2+1): Distribute (a-1) across the terms: (a-1)(a^2+1) = a(a^2+1) - 1(a^2+1) = a^3 + a - a^2 - 1

3. Simplifying (a+3)(a^2-1): Distribute (a+3) across the terms: (a+3)(a^2-1) = a(a^2-1) + 3(a^2-1) = a^3 - a + 3a^2 - 3

Now we can combine these simplified expressions:

2(a+1)(a^2+1) - (a-1)(a^2+1) - (a+3)(a^2-1) = 2a^3 + 2a + 2a^2 + 2 - (a^3 + a - a^2 - 1) - (a^3 - a + 3a^2 - 3) = 2a^3 + 2a + 2a^2 + 2 - a^3 - a + a^2 + 1 - a^3 + a - 3a^2 + 3

Now let's simplify the second expression:

(n-1)(n-2) - (n+3)(n-2) + (n+3)(n+2) = (n^2 - 3n + 2) - (n^2 + n - 6) + (n^2 + 5n + 6) = n^2 - 3n + 2 - n^2 - n + 6 + n^2 + 5n + 6

Now we can combine these simplified expressions:

(2a^3 + 2a + 2a^2 + 2 - a^3 - a + a^2 + 1 - a^3 + a - 3a^2 + 3) - (n^2 - 3n + 2 - n^2 - n + 6 + n^2 + 5n + 6) = 2a^3 - a^3 - a^3 + 2a^2 - 3a^2 - 3a^2 + 2a + a - 5n = -a^3 - 4a^2 + 3a - 5n

Therefore, the simplified expression is -a^3 - 4a^2 + 3a - 5n.