Find the perfect square:

w^2-4w+=

4

Step-by-step explanation:

You need to find a value that makes this expression a perfect square trinomial.  A perfect square trinomial results from squaring a binomial from the form of (a + b)².  

When we square (a + b)², we get  a² + 2ab + b²   (expand and use foil)

Break this into three steps.

Step 1:  square the first term   (this is where a² came from)

Step 2:  Multipy the terms together, then multiply by 2

             (a)(b) = ab, then we multiply by 2, giving is 2ab.

Step 3:  Square the second term (This is where b² came from)

So we will use these steps to work backwards to get our answer.  

Using w² - 4w + k, we need to find a value for k that makes this a perfect square trinomial.

Remember, we are working backwards now, so we do the opposite operation form the steps above

Step 1:  We take the square root of the first term   (√w² = w)

Step 2:  First divide the second term by 2, the result is the product of the 2

               terms.   (-4w/2 = -2w, so our terms are w and -2)

Step 3:  We are given the third term by step 2.  Since the first term is w, and the product of the first and second term is -2w, the third term must be -2.  

So we square -2 to get the third term in our trinomial.  (-2)² = 4