Use the polynomial identity x^2+2ax+a^2=(x+a)(x+a) to rewrite x^2+4x+4. Which polynomial does this establish?(1 point)
1. x^2+4x+4=(x+2)(x+2)
2. x^2+4x+4=(x+4)(x+4)
3. x^2+4x+4=(x-4)(x-4)
4. x^2+4x+4=(x-2)(x-2)
The polynomial x^2+4x+4 can be rewritten as (x+2)(x+2). Thus, the correct answer is:
1. x^2+4x+4=(x+2)(x+2)
To rewrite x^2+4x+4 using the given polynomial identity x^2+2ax+a^2=(x+a)(x+a), we need to find the value of a.
In this case, 2a = 4, so a = 2.
Now, substituting a = 2 into the polynomial identity, we have:
x^2 + 2(2)x + (2^2) = (x+2)(x+2)
Simplifying further:
x^2 + 4x + 4 = (x+2)(x+2)
Therefore, the correct answer is:
1. x^2+4x+4=(x+2)(x+2)