Factoring trinomial perfect square trinomial pst x²+4×+4 what is the correct answer with explaination step by step solution

To factor the trinomial \( x^2 + 4x + 4 \), let's follow the steps to identify whether it is a perfect square trinomial and then factor it accordingly.

### Step 1: Recognize the trinomial structure
A perfect square trinomial has the form:
\[ a^2 + 2ab + b^2 \]
Where \( a \) and \( b \) are numbers or variables.

In this case, the trinomial is \( x^2 + 4x + 4 \).

### Step 2: Identify \( a \) and \( b \)
Compare \( x^2 + 4x + 4 \) with the perfect square trinomial form \( a^2 + 2ab + b^2 \):
- \( a^2 = x^2 \) implies \( a = x \).
- The middle term is \( 2ab = 4x \). Since \( a = x \), we can find \( b \) by solving:
  \[ 2b = 4 \quad \Rightarrow \quad b = \frac{4}{2} = 2 \]

### Step 3: Confirm the perfect square structure
The last term \( b^2 \) in the perfect square trinomial should be \( b^2 = 2^2 = 4 \). This matches the last term in the original trinomial, confirming that the trinomial is indeed a perfect square trinomial.

### Step 4: Write the trinomial as a square of a binomial
Since \( a = x \) and \( b = 2 \), the trinomial can be factored as:
\[ x^2 + 4x + 4 = (x + 2)^2 \]

### Final Answer:
The correct factorization of \( x^2 + 4x + 4 \) is:
\[
(x + 2)^2
\]

Would you like more details or have any questions about this process?

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Here are 5 related questions to expand on this topic:
1. How do you factor a trinomial that is not a perfect square?
2. Can you factor \( x^2 + 4x + 4 \) using a different method, such as completing the square?
3. What is the general formula for factoring the difference of squares?
4. How do you recognize when a trinomial is not factorable over the integers?
5. What are some common mistakes to avoid when factoring trinomials?

**Tip:** Always check if the trinomial is a perfect square by comparing it with the form \( a^2 + 2ab + b^2 \). This can save time and ensure accuracy.

Factoring trinomial perfect square trinomial pst x²+4x+4 what is the correct answer with explanation step by step solution

Learn how to factor the perfect square trinomial x² + 4x + 4 with a clear, step-by-step solution. This algebra problem demonstrates how to identify and factor perfect square trinomials using key formulas. Ideal for students in Grades 8-10.

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