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Step-by-step explanation:
To determine if the given expression is divisible by 8, we can simplify it first and then check if the result is divisible by 8.
The given expression is: (2m+4)^2+(2m+2)^2-4
Let's simplify each term separately:
(2m+4)^2 = (2m+4)(2m+4) = 4m^2 + 16m + 16
(2m+2)^2 = (2m+2)(2m+2) = 4m^2 + 8m + 4
Now, let's add these two simplified terms:
(4m^2 + 16m + 16) + (4m^2 + 8m + 4) = 8m^2 + 24m + 20
Finally, let's subtract 4 from the sum:
8m^2 + 24m + 20 - 4 = 8m^2 + 24m + 16
Now we need to check if this result is divisible by 8. If it is, then the original expression is also divisible by 8.
To be divisible by 8, a number must be divisible by both 2 and 4. Let's check for both:
1. Divisibility by 2: The expression is divisible by 2 if the last digit is even (0, 2, 4, 6, or 8). In this case, the last digit is 6, which is even, so the expression is divisible by 2.
2. Divisibility by 4: A number is divisible by 4 if the last two digits form a number that is divisible by 4. In this case, the last two digits are 16, which is divisible by 4. Therefore, the expression is divisible by 4.
Since the expression is divisible by both 2 and 4, it is divisible by 8.