Let's analyze the given equation step-by-step to determine which property it demonstrates:
Given equation:
[tex]\[ x^2 + 2x = 2x + x^2 \][/tex]
To understand which property this equation showcases, let's observe the left-hand side and the right-hand side terms and how they relate to each other.
1. Identify the terms on both sides:
- Left-hand side: [tex]\( x^2 + 2x \)[/tex]
- Right-hand side: [tex]\( 2x + x^2 \)[/tex]
2. Compare the terms:
- Both sides of the equation contain the same terms, [tex]\( x^2 \)[/tex] and [tex]\( 2x \)[/tex], but the order of the terms is different.
3. Evaluate the order of terms:
- On the left-hand side, the terms are [tex]\( x^2 \)[/tex] followed by [tex]\( 2x \)[/tex].
- On the right-hand side, the terms are [tex]\( 2x \)[/tex] followed by [tex]\( x^2 \)[/tex].
The equation demonstrates that the order in which we add the terms does not affect the result. This characteristic behavior is known as the commutative property of addition. The commutative property of addition states that changing the order of the addends (terms being added) does not change the sum.
Thus, the equation:
[tex]\[ x^2 + 2x = 2x + x^2 \][/tex]
demonstrates the commutative property.
