Factor 16a^2-8a+1

Problem

16*a^2−8*a+1

Solution

1. Identify the structure of the quadratic expression, which is in the form A*x^2+B*x+C

2. Recognize that the first term 16*a^2 is a perfect square, (4*a)^2 and the last term 1 is also a perfect square, 1^2

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

4. Verify the middle term by calculating $2(4a)(1) = 8a$, which matches the given expression's middle term.

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

Final Answer

16*a^2−8*a+1=(4*a−1)^2

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