Factor 4x^2+16x+16

Problem

4*x2+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*(x2+4*x+4)

3. Recognize the quadratic expression inside the parentheses as a perfect square trinomial of the form a2+2*a*b+b2

4. Apply the formula (a+b)2=a2+2*a*b+b2 where a=x and b=2

4*(x+2)2

Final Answer

4*x2+16*x+16=4*(x+2)2

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