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

Problem

y2+18*x*y+81*x2

Solution

1. Identify the structure of the trinomial as a potential perfect square trinomial of the form a2+2*a*b+b2

2. Determine the square roots of the first and last terms, where a2=y2 gives a=y and b2=81*x2 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, a2+2*a*b+b2=(a+b)2 using the identified values.

Final Answer

y2+18*x*y+81*x2=(y+9*x)2

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