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

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.

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