Factor y^2+14y+49

Problem

y2+14*y+49

Solution

1. Identify the structure of the quadratic expression, which is in the form a*y2+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 y2 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, a2+2*a*b+b2=(a+b)2

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

Final Answer

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

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