Factor 4x^2+16x+16

Problem

4*x^2+16*x+16

Solution

1. Identify the greatest common factor (GCF) for all terms in the expression.

2. Factor out the GCF, which is 4

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

3. Recognize the quadratic expression inside the parentheses as a perfect square trinomial of the form a^2+2*a*b+b^2

4. Apply the formula (a+b)^2=a^2+2*a*b+b^2 where a=x and b=2

4*(x+2)^2

Final Answer

4*x^2+16*x+16=4*(x+2)^2

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