Factor y^2+14y+49

Problem

y^2+14*y+49

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y^2+b*y+c where a=1 b=14 and c=49

2. Recognize that the expression is a perfect square trinomial because the first term y^2 is (y)^2 the last term 49 is (7)^2 and the middle term 14*y is 2*(y)*(7)

3. Apply the formula for a perfect square trinomial, a^2+2*a*b+b^2=(a+b)^2

4. Substitute y for a and 7 for b into the binomial square form.

Final Answer

y^2+14*y+49=(y+7)^2

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