Factor x^2+4x+4

Problem

x^2+4*x+4

Solution

1. Identify the expression as a quadratic trinomial of the form a*x^2+b*x+c where a=1 b=4 and c=4

2. Recognize that the expression follows the perfect square trinomial pattern a^2+2*a*b+b^2=(a+b)^2

3. Determine the values for the pattern by noting that x^2 is (x)^2 and 4 is (2)^2

4. Verify the middle term by calculating $2(x)(2) = 4x$, which matches the given expression.

5. Apply the formula for a perfect square trinomial to write the factored form.

Final Answer

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

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