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.
