Question

(n+4)²+7n2 ділиться націло на 8

Answer 1

((n+4)² + 7n²) ÷ 8 = (n² + 8n + 16 + 7n²) ÷ 8 = (8n² + 8n + 16) ÷ 8 = n² + n + 2

Ответ: да

Answer 2

To check if the expression (n+4)² + 7n² is divisible by 8, we need to find the remainder when this expression is divided by 8. If the remainder is 0, then it is divisible by 8.

Let's simplify the expression first:

(n + 4)² + 7n² = (n + 4)(n + 4) + 7n² = n² + 8n + 16 + 7n² = 8n² + 8n + 16

Now, we need to find the remainder when 8n² + 8n + 16 is divided by 8. We can do this by substituting some integer values of n and observing the pattern:

Let's try n = 0: 8(0)² + 8(0) + 16 = 16, which leaves a remainder of 0 when divided by 8.

Now, let's try n = 1: 8(1)² + 8(1) + 16 = 32, which leaves a remainder of 0 when divided by 8.

Now, let's try n = 2: 8(2)² + 8(2) + 16 = 64, which leaves a remainder of 0 when divided by 8.

Based on these observations, it seems that for any integer value of n, the expression 8n² + 8n + 16 will always leave a remainder of 0 when divided by 8. Therefore, the expression (n + 4)² + 7n² is divisible by 8.