Factor y^2+14xy+49x^2

Problem

y2+14*x*y+49*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 the square of y and the last term 49*x2 is the square of 7*x

3. Check the middle term to see if it fits the pattern of a perfect square trinomial, a2+2*a*b+b2=(a+b)2

4. Verify the middle term by calculating 2*(y)*(7*x) which equals 14*x*y

5. Apply the formula for a perfect square trinomial using a=y and b=7*x

Final Answer

y2+14*x*y+49*x2=(y+7*x)2

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