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Home >> Algebraic Expression >> Variables >> Multiplication of Variables >>

Multiplication of Variables

Coefficient Of Variable Power of Variable Multiplication of Variables

Before you study what is multiplication of variables, you are advised to read:

What are Variables ?

You will also face following situation under this concept:

  • Multiplication of Two or more Positive Variables
  • Multiplication of Two Negative Variables
  • Multiplication of Three or more Negative Variables
  • Multiplication of Positive and Negative Variables

    Multiplication of Two or More Positive Variables

    Example 1: Multiple x and y
    Solution: In the given question:
    x and y are both variables

    Multiplication expression gives us:
    x X y

    On solving the multiplication expression, we get:
    xy

    Hence, multiplication of (x) and (y) give us (xy)



    Example 2: Multiple b and a
    Solution: In the given question:
    b and a are both variables

    Multiplication expression gives us:
    b X a

    On solving the multiplication expression, we get:
    ba

    or we write it as
    ab (because variable are arranged in alphabetical order)

    Hence, multiplication of (b) and (a) give us (ab)



    Example 3: Multiple z, y and x
    Solution: In the given question:
    z, y and x are variables

    Multiplication expression gives us:
    z X y X x

    On solving the multiplication expression, we get:
    zyx

    or we write it as
    xyz (because variable are arranged in alphabetical order)

    Hence, multiplication of (z), (y) and (x) give us (xyz)


    Multiplication of Two Negative Variables:
    (This is similar to Multiplication of Two Negative Integers)


    Example 4: Multiply (-M) and (-N)
    Solution: In the given question:
    (-M) and (-N) are negative variables
    Multiplication expression gives us:
    (-M) X (-N)

    Now, we have two negative variable i.e. (-M) and (-N)
    So we will multiply (M) and (N) (as explained in example 1, 2 and 3) and put positive sign or addition operator to the left of product & we get:
    +MN

    Or we can write it as:
    MN

    Hence, Multiplication of (-N) and (-M) give us (MN)

    Multiplication of Three or more Negative Variables
    (This is similar to Multiplication of Three or more Negative Integers )


    Example 5: Multiply (-p), (-q) and (-r)
    Solution: In the given question:
    (-p), (-q) and (-r) are negative variables
    Multiplication expression gives us:
    (-p) X (-q) X (-r)

    Now, we have three negative variables i.e. (-p), (-q) and (-r)
    So we will multiply these variables (as explained in example 1, 2 and 3) and ignore negative sign or subtraction operator & we get:
    pqr

    Now we put negative sign or subtraction operator i.e. (-) to the left of (pqr) & we get:
    (-pqr)

    Hence, Multiplication of (-p), (-q) and (-r) give us (-pqr)

    Example 6: Multiply (- a), (-b), (-c) and (-d)
    Solution: In the given question:
    (-a), (-b), (-c) and (-d) are negative variables
    Multiplication expression gives us:
    (-a) X (-b) X (-c) X (-d)

    Now, we have four negative variables i.e. (- a), (-b), (-c) and (-d)
    So we will multiply these variables (as explained in example 1, 2 and 3) and put positive sign or addition operator to the left of product & we get:
    +abcd

    Or we can write it as:
    abcd

    Hence, Multiplication of (- a), (-b), (-c) and (-d) give us (abcd)


    Multiplication of Positive and Negative Variables
    (This is similar to Multiplication of Positive and Negative Integer)

    Example 7: Multiply (x) and (-y)
    Solution: In the given question:
    x is a positive variable
    (-y) is a negative variable

    Multiplication expression gives us:
    x X (-y)

    Now, we have one positive variable i.e. (x) and one negative variable i.e. (-y)
    So we will multiply these variables (as explained in example 1, 2 and 3) and ignore negative sign or subtraction operator i.e. (-) & we get:
    xy

    Now we put negative sign or subtraction operator i.e. (-) to the left of (xy) & we get:
    (-xy)

    Hence, Multiplication of (x) and (-y) give us (-xy)

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