Multiplying a Monomial by a Monomial
Multiplying two monomials
Some more useful examples follow.
(ii)Try these
Multiplying three or more monomials
Observe the following examples.
(i) 4xy ×
- The algebra expression is 4xy ×
5 x 2 y 2 6 x 3 y 3 - multiply with x terms and y terms
x 3 y 3 x 3 y 3 - Divide the terms and multiply with values
( x 3 x 3 y 3 y 3 - Calculate the x terms and y terms separately 120
x - We have found the answer.
Similarly,
(ii) 2x × 5y × 7z = (2x × 5y) × 7z =
It is clear that we, first multiply the first two monomials and then multiply the resulting monomial by the third monomial. This method can be extended to the product of any number of monomials.
We can find the product in other way also.
4xy ×
Try These
Find 4x × 5y × 7z
Method 1: First find 4x × 5y and multiply it by 7z
4x × 5y = (4×5)×(x×y) =
20xy × 7z = (20×7) × (xy×z) =
Method 2: First find 5y × 7z and multiply it by 4x.
5y × 7z = (5×7) × (y×z) =
4x × 35yz = (4×35) × (x×yz) =
Is the result the same? What do you observe?
Does the order in which you carry out the multiplication matter?
Example 3: Complete the table for area of a rectangle with given length and breadth.
Solution
| length | breadth | area |
|---|---|---|
| 3x | 5y | 3x × 5y = |
| 9y | 9y x 4 | |
| 4ab | 5bc | 4ab x 5bc = |
Example 4: Find the volume of each rectangular box with given length, breadth and height.
| No | length | breadth | height |
|---|---|---|---|
| (i) | 2ax | 3by | 5cz |
| (ii) | |||
| (iii) | 2q | 4 | 8 |