Factor y^2+10xy+25x^2

Problem

y^2+10*x*y+25*x^2

Solution

1. Identify the structure of the expression as a quadratic trinomial in terms of y and x

2. Recognize that the first term y^2 is a perfect square of y and the last term 25*x^2 is a perfect square of 5*x

3. Check if the middle term 10*x*y matches the pattern for a perfect square trinomial a^2+2*a*b+b^2 where a=y and b=5*x

4. Verify the middle term calculation:

2*(y)*(5*x)=10*x*y

5. Apply the formula for a perfect square trinomial (a+b)^2=a^2+2*a*b+b^2 to write the factored form.

Final Answer

y^2+10*x*y+25*x^2=(y+5*x)^2

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