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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)