Question

1. factor the perfect square trinomial ( y^2 - 14y + 49 ).

Explanation:

Step1: Recall perfect square formula

The formula for a perfect square trinomial is \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Identify \(a\) and \(b\)

In the trinomial \(y^2-14y + 49\), we have \(a = y\) (since \(a^2=y^2\)), and for the middle term, \(-2ab=-14y\). Substituting \(a = y\) into \(-2ab=-14y\), we get \(-2\times y\times b=-14y\), which simplifies to \(-2b=-14\), so \(b = 7\). Also, \(b^2 = 49\) (which matches the constant term).

Step3: Apply the formula

Using the perfect square formula \(a^2-2ab + b^2=(a - b)^2\) with \(a = y\) and \(b = 7\), we get \(y^2-14y + 49=(y - 7)^2\).

Answer:

\((y - 7)^2\)