Factor b^2+16b+64

Problem

b^2+16*b+64

Solution

1. Identify the structure of the trinomial, which is in the form a*x^2+b*x+c

2. Recognize that the first term b^2 is a perfect square of b and the last term 64 is a perfect square of 8

3. Check if the middle term 16*b matches the pattern 2*a*b for a perfect square trinomial (a+b)^2

4. Verify the calculation: 2⋅b⋅8=16*b which matches the middle term.

5. Apply the formula for a perfect square trinomial a^2+2*a*b+b^2=(a+b)^2

Final Answer

b^2+16*b+64=(b+8)^2

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