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29 April, 08:55

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

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  1. 29 April, 09:25
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    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.
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