Questions: Factor the trinomial. x^2 + 4x + 4 =

Factor the trinomial. x^2 + 4x + 4 =
Transcript text: Factor the trinomial. \[ x^{2}+4 x+4= \]
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Solution

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Solution Steps

Step 1: Identify the trinomial

The given trinomial is \( x^{2} + 4x + 4 \).

Step 2: Check if it is a perfect square trinomial

A perfect square trinomial has the form \( (x + a)^{2} = x^{2} + 2ax + a^{2} \). Compare this with the given trinomial:

  • \( x^{2} \) matches \( x^{2} \).
  • \( 4x \) matches \( 2ax \) when \( a = 2 \).
  • \( 4 \) matches \( a^{2} \) when \( a = 2 \).
Step 3: Factor the trinomial

Since the trinomial matches the perfect square form, it can be factored as: \[ x^{2} + 4x + 4 = (x + 2)^{2}. \]

Final Answer

\(\boxed{(x + 2)^{2}}\)

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