Factor y^2+18y+81

Problem

y2+18*y+81

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y2+b*y+c where a=1 b=18 and c=81

2. Recognize that the expression is a perfect square trinomial because the first term y2 is the square of y the last term 81 is the square of 9 and the middle term 18*y is twice the product of y and 9

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

4. Substitute y for a and 9 for b into the formula to obtain the factored form.

Final Answer

y2+18*y+81=(y+9)2

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