We are given the area of a square which means that the expression we are given is a perfect square trinomial.
|3x-7|
Practice makes perfect
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)^2
Let'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.
