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

Problem

y2+10*x*y+25*x2

Solution

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

2. Recognize that the first term y2 is a perfect square of y and the last term 25*x2 is a perfect square of 5*x

3. Check if the middle term 10*x*y matches the pattern for a perfect square trinomial a2+2*a*b+b2 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=a2+2*a*b+b2 to write the factored form.

Final Answer

y2+10*x*y+25*x2=(y+5*x)2

Want more problems? Check here!