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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