To identify which equation is represented by the model, let's analyze each given option step-by-step and compare them to the correct expression for a perfect square monomial.
1. Option 1: [tex]\((2x)^2 = 4x^2\)[/tex]
Let's expand this expression to see if it matches:
[tex]\[
(2x)^2 = (2 \cdot x)^2 = 2^2 \cdot x^2 = 4x^2
\][/tex]
This simplifies to:
[tex]\[
(2x)^2 = 4x^2
\][/tex]
This equation is correctly simplified.
2. Option 2: [tex]\(\left(2x^2\right)^2 = 4x^4\)[/tex]
Let's expand this expression to see if it matches:
[tex]\[
\left(2x^2\right)^2 = (2 \cdot x^2)^2 = 2^2 \cdot (x^2)^2 = 4 \cdot x^4 = 4x^4
\][/tex]
This simplifies to:
[tex]\[
\left(2x^2\right)^2 = 4x^4
\][/tex]
Although it simplifies correctly, it does not match our original perfect square monomial model which was given as [tex]\((2x)^2\)[/tex].
3. Option 3: [tex]\((4x)^2 = 8x^2\)[/tex]
Let's expand this expression to see if it matches:
[tex]\[
(4x)^2 = 4^2 \cdot x^2 = 16x^2
\][/tex]
This simplifies to:
[tex]\[
(4x)^2 = 16x^2 \neq 8x^2
\][/tex]
This equation does not simplify correctly.
Out of the three options, only Option 1: [tex]\((2x)^2 = 4x^2\)[/tex] represents the correct equation for our perfect square monomial model.
Therefore, the equation represented by the model is:
[tex]\[
(2x)^2 = 4x^2
\][/tex]
