Question

which property does each equation demonstrate?
$x^2 + 2x = 2x + x^2$

$(3x^4 + 2x^3) - (2x^4 + x^3) = x^4 + x^3$

$(2x^2 + 7x) + (2y^2 + 6y) = (2y^2 + 6y) + (2x^2 + 7x)$

Explanation:

1. For $x^2 + 2x = 2x + x^2$, the order of the terms being added is swapped without changing the sum, which matches the definition of the commutative property of addition.
2. For $(3z^4 + 2z^3) - (2z^4 + z^3) = z^4 + z^3$, like terms (terms with the same variable and exponent) are combined by subtracting their coefficients, demonstrating the combining like terms property.
3. For $(2x^2 + 7x) + (2y^2 + 6y) = (2y^2 + 6y) + (2x^2 + 7x)$, the order of the two polynomial addends is swapped without changing the total sum, which is the commutative property of addition applied to polynomial addition.

Answer:

1. Commutative Property of Addition
2. Combining Like Terms
3. Commutative Property of Addition