Factor 49x^2-70x+25

Problem

49*x2−70*x+25

Solution

1. Identify the structure of the expression 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.

a=√(,49*x2)=7*x

b=√(,25)=5

3. Verify the middle term by calculating 2*a*b

2*(7*x)*(5)=70*x

4. Apply the formula for a perfect square trinomial, which is a2−2*a*b+b2=(a−b)2

(7*x−5)2

Final Answer

49*x2−70*x+25=(7*x−5)2

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