Factor y^2+4y+4

Problem

y^2+4*y+4

Solution

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

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

3. Determine the square roots of the first and last terms: √(,y^2)=y and √(,4)=2

4. Verify the middle term by calculating 2⋅y⋅2=4*y which matches the given expression.

5. Write the factored form as the square of the sum of these roots.

Final Answer

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

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