Factor 49x^2-14x+1

Problem

49*x2−14*x+1

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x2+b*x+c

2. Recognize that the first term 49*x2 is a perfect square, (7*x)2 and the last term 1 is also a perfect square, 1

3. Check if the middle term fits the pattern for a perfect square trinomial a2−2*a*b+b2 where a=7*x and b=1

4. Verify the middle term calculation: 2(7x)(1) = 14x.S*i*n*c*e*t*h*e*m*i*d(d(l))*e*t*e*r*m*i*s()14x,t*h*e*e*x*p*r*e*s(s(i))*o*n*m*a*t*c*h*e*s(t)*h*e*p*a*t*t*e*r*na - b)^2$.

5. Apply the formula for a perfect square trinomial: a2−2*a*b+b2=(a−b)2

Final Answer

49*x2−14*x+1=(7*x−1)2

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