Factor 16x^2+8x+1

Problem

16*x^2+8*x+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*x^2 is a perfect square, (4*x)^2 and the last term 1 is also a perfect square, 1^2

3. Check if the middle term 8*x fits the pattern 2*a*b for the perfect square trinomial formula a^2+2*a*b+b^2=(a+b)^2

4. Verify the middle term by calculating $2(4x)(1) = 8x$.

5. Apply the formula for a perfect square trinomial using a=4*x and b=1

Final Answer

16*x^2+8*x+1=(4*x+1)^2

Want more problems? Check here!