Question

Does the order of variables matter when combining like terms in algebra

Answer 1

Answer: No
The order of variables does not matter when combining like terms in algebra, because of the commutative property.

Explanation:
Consider the addition of two algebraic expressions.
f(x) = x³ - 5x² + 3x - 2
g(x) = 6x³ + 10x² - 7x + 9

Add f(x) and g(x).
f(x) + g(x) = x³ - 5x² + 3x - 2 + (6x³ + 10x² - 7x + 9)
                = x³ + 6x³ - 5x² + 10x² + 3x - 7x - 2 + 9
                = 7x³ + 5x² - 4x + 7

Now add g(x) and f(x) in order to change the order of variable addition.
g(x) + f(x) = 6x³ + 10x² - 7x + 9 + (x³ - 5x² + 3x - 2)
                = 6x³ + x³ + 10x² - 5x² - 7x + 3x + 9 - 2
                = 7x³ + 5x² - 4x + 7

The two additions yield the same result, although the order of variable was reversed during the addition.

In general, algebraic operations are commutative.