Factor 49x^2-56x+16

Problem

49*x2−56*x+16

Solution

1. Identify the structure of the quadratic expression, noting that the first and last terms are perfect squares.

2. Determine the square roots of the leading term and the constant term: √(,49*x2)=7*x and √(,16)=4

3. Verify if the middle term fits the pattern for a perfect square trinomial, a2−2*a*b+b2=(a−b)2 by checking if 2(7x)(4) = 56x$.

4. Apply the formula for a perfect square trinomial using a=7*x and b=4

Final Answer

49*x2−56*x+16=(7*x−4)2

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