Factor y^2-6y+9

Problem

y^2−6*y+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y^2+b*y+c where a=1 b=−6 and c=9

2. Recognize that the expression is a perfect square trinomial because the first term y^2 is (y)^2 the last term 9 is (−3)^2 and the middle term −6*y is 2*(y)*(−3)

3. Apply the formula for a perfect square trinomial, which states that a^2−2*a*b+b^2=(a−b)^2

4. Substitute the values into the formula where a=y and b=3

Final Answer

y^2−6*y+9=(y−3)^2

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