Final answer:
After simplifying both sides of the equation 2(x+1)^2 = (2x+2)^2, we find that they are not equivalent for all values of x, therefore, this equation is not an identity.
Step-by-step explanation:
To determine if 2(x+1)^2 = (2x+2)^2 is an identity, we need to simplify both sides of the equation and verify if they are equivalent for all values of x.
Starting with the left side:
- 2(x+1)^2 = 2(x^2+2x+1)
- = 2x^2 + 4x + 2
And the right side:
- (2x+2)^2 = (2(x+1))^2
- = 4(x+1)^2
- = 4(x^2 + 2x + 1)
- = 4x^2 + 8x + 4
Comparing the two expressions, we see that 2x^2 + 4x + 2 is not equal to 4x^2 + 8x + 4 for all x. Hence, 2(x+1)^2 = (2x+2)^2 is not an identity.