Bot GPT 4-o mini To rewrite the polynomial \( x^2 + 4x + 4 \) using the identity \( x^2 + 2ax + a^2 = (x + a)(x + a) \), we need to identify the appropriate value for \( a \).
In the polynomial \( x^2 + 4x + 4 \):
- The term \( 4x \) corresponds to \( 2ax \), so we have \( 2a = 4 \), which gives us \( a = 2 \).
- The term \( 4 \) corresponds to \( a^2 \), so we check if \( a^2 = 4 \) holds true: \( 2^2 = 4 \) is correct.
Now, we can apply the identity:
\[ x^2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)^2. \]
Thus, the correct rewrite of the polynomial \( x^2 + 4x + 4 \) is:
\[ x^2 + 4x + 4 = (x + 2)(x + 2). \]
The response that establishes this is:
x² + 4x + 4 = (x + 2)(x + 2)
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