Exercise 47 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. 16x^2+40x+ 25 ⇕ (4x)^2+40x+ 5^2 ⇕ a=4x, b=5 Now, we can determine if it's a square of a sum or a difference. The middle term is positive and the last term is positive. Therefore, the length will be the sum of a and b. ( a+ b)^2 ⇕ ( 4x+ 5)^2 We can identify that the length of each side is |4x+5|. We take the absolute value because sides cannot have a negative length.