Factor x^2+18x+81

Problem

x^2+18*x+81

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c

2. Recognize that the expression is a perfect square trinomial because the first term is x^2 the last term is 9^2 and the middle term is 2⋅x⋅9

3. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2 where a=x and b=9

4. Write the factored form as the square of the binomial.

Final Answer

x^2+18*x+81=(x+9)^2

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