Factor 36x^2-84x+49

Problem

36*x2−84*x+49

Solution

1. Identify the structure of the trinomial. Notice that the first term 36*x2 and the last term 49 are both perfect squares.

2. Determine the square roots of the perfect squares. The square root of 36*x2 is 6*x and the square root of 49 is 7

3. Check if the middle term matches the pattern for a perfect square trinomial, which is 2*a*b

4. Calculate the product 2⋅(6*x)⋅(7)

2⋅6*x⋅7=84*x

5. Verify the sign of the middle term. Since the middle term is −84*x the expression follows the pattern a2−2*a*b+b2=(a−b)2

6. Write the factored form using a=6*x and b=7

Final Answer

36*x2−84*x+49=(6*x−7)2

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