Exercise 46 Page 69

We are given the area of a square which means that the expression we are given is a perfect square trinomial. This means that the given expression can be rewritten as a square. a^2+2ab+b^2=(a+b)^2 or a^2-2ab+b^2=(a-b)^2Let's begin by rewriting the first and last terms of the expression as squares in order to identify a and b. 9x^2-42x+ 49 ⇕ (3x)^2-42x+ 7^2 ⇕ a=3x, b=7 Now, we can determine if it's a square of a sum or a difference. The middle term is negative and the last term is positive. Therefore, the length will be the difference of a and b. ( a- b)^2 ⇕ ( 3x- 7)^2 We can identify that the length of each side is |3x-7|. We take the absolute value because sides cannot have a negative length.