We are given the area of a square which means that the expression we are given is a perfect square trinomial.
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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.
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.
