Question

Use the polynomial identity x2+2ax+a2=(x+a)(x+a) to rewrite x2+4x+4. Which polynomial does this establish?(1 point)
Responses

x2+4x+4=(x+4)(x+4)
x squared plus 4 x plus 4 equals left parenthesis x plus 4 right parenthesis left parenthesis x plus 4 right parenthesis

x2+4x+4=(x−2)(x−2)
x squared plus 4 x plus 4 equals left parenthesis x minus 2 right parenthesis left parenthesis x minus 2 right parenthesis

x2+4x+4=(x−4)(x−4)
x squared plus 4 x plus 4 equals left parenthesis x minus 4 right parenthesis left parenthesis x minus 4 right parenthesis

x2+4x+4=(x+2)(x+2)

Answer 1

To rewrite the polynomial \( x^2 + 4x + 4 \) using the polynomial identity \( x^2 + 2ax + a^2 = (x + a)(x + a) \), we need to identify \( 2a \) and \( a^2 \) in the expression.

In the given polynomial \( x^2 + 4x + 4 \):

- The coefficient of \( x \) is \( 4 \).
- The constant term is \( 4 \).

We can identify \( 2a \) and \( a^2 \) as follows:

- Since \( 2a = 4 \), we have \( a = 2 \).
- Since \( a^2 = 4 \), we can also verify that \( 2^2 = 4 \).

Applying the identity:

\[
x^2 + 4x + 4 = x^2 + 2(2)x + 2^2 = (x + 2)(x + 2)
\]

Thus, we can write:

\[
x^2 + 4x + 4 = (x + 2)(x + 2)
\]

Therefore, the correct response is:

**\( x^2 + 4x + 4 = (x + 2)(x + 2) \)**.