Factor y^2+18xy+81x^2

Problem

y^2+18*x*y+81*x^2

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a^2+2*a*b+b^2

2. Determine the square roots of the first and last terms, where a^2=y^2 gives a=y and b^2=81*x^2 gives b=9*x

3. Verify the middle term by calculating 2*a*b which is $2(y)(9x) = 18xy$.

4. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2 using the identified values.

Final Answer

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

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