Factor 16x^2-56x+49

Problem

16*x2−56*x+49

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a2−2*a*b+b2

2. Determine the square roots of the first and last terms to find a and b

3. Calculate the first term's root:

√(,16*x2)=4*x

4. Calculate the last term's root:

√(,49)=7

5. Verify the middle term by checking if 2*a*b matches 56*x

2*(4*x)*(7)=56*x

6. Apply the formula for a perfect square trinomial (a−b)2

(4*x−7)2

Final Answer

16*x2−56*x+49=(4*x−7)2

Want more problems? Check here!