Factor 49x^2-28x+4

Problem

49*x2−28*x+4

Solution

1. Identify the expression as a quadratic trinomial of the form a*x2+b*x+c where a=49 b=−28 and c=4

2. Recognize that the first and last terms are perfect squares: 49*x2=(7*x)2 and 4=2

3. Check if the middle term fits the pattern for a perfect square trinomial, a2−2*a*b+b2=(a−b)2 by calculating 2*(7*x)*(2)

4. Verify the calculation: 2⋅7*x⋅2=28*x which matches the middle term of the expression.

5. Apply the formula for a perfect square trinomial (a−b)2 using a=7*x and b=2

Final Answer

49*x2−28*x+4=(7*x−2)2

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