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

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.