Question

fill in the blank with a number to make the expression a perfect square.
$w^2 - 2w + \square$

Explanation:

Step1: Recall perfect square formula

A perfect square trinomial has the form \(a^2 - 2ab + b^2=(a - b)^2\). For the expression \(w^2-2w+\square\), here \(a = w\) and \(-2ab=-2w\).

Step2: Solve for \(b\)

Substitute \(a = w\) into \(-2ab=-2w\), we get \(-2\times w\times b=-2w\). Divide both sides by \(-2w\) (assuming \(w
eq0\)), we find \(b = 1\).

Step3: Find the constant term

The constant term of the perfect square trinomial is \(b^2\). Since \(b = 1\), then \(b^2=1^2 = 1\). So the blank should be filled with 1.

Answer:

1