The distributive law states that multiplying a group of terms by a number is the same as multiplying each term separately by that same number and adding the products.
For example, let's take a look at the following expression:
We can evaluate this expression using the distributive law:
Therefore,
The distributive law also applies when the multiplication occurs on the right of the parentheses:
Expand
Using the distributive law, we multiply each term inside the parentheses by the number
$5(8x + 3)=$
|
a
|
$-40x - 15$ |
|
b
|
$13x + 8$ |
|
c
|
$-40x + 15$ |
|
d
|
$40x + 15$ |
|
e
|
$40x - 15$ |
$(2 + 5x) \cdot 3=$
|
a
|
$23 + 53x$ |
|
b
|
$6 + 15x$ |
|
c
|
$5 + 8x$ |
|
d
|
$2 + 15x$ |
|
e
|
$6 + 5x$ |
Expand
Using the distributive law, we multiply each term inside the parentheses by the number
$-2(3x+1)=$
|
a
|
$-6x+1$ |
|
b
|
$-6x+2$ |
|
c
|
$-6x-2$ |
|
d
|
$-23x-21$ |
|
e
|
$x-1$ |
$(9n+8)\cdot(-5)=$
|
a
|
$-45n-40$ |
|
b
|
$45n-40$ |
|
c
|
$45n-13$ |
|
d
|
$-45n-13$ |
|
e
|
$45n+40$ |
The distributive law also works when there is subtraction inside the parentheses.
For example, we can expand the expression as follows:
Notice that we keep a plus () sign between the two terms. This helps us to avoid mistakes when multiplying with negative numbers.
Now, evaluating our expression, we have
Finally, the distributive law also applies when the multiplication occurs on the right of the parentheses:
Expand
Using the distributive law, we multiply each term inside the parentheses by the number
$5(3a - 2b) =$
|
a
|
$5a-2b$ |
|
b
|
$-15a+10b$ |
|
c
|
$15a+10b$ |
|
d
|
$53a-52b$ |
|
e
|
$15a-10b$ |
$(4x - 1) \cdot 9=$
|
a
|
$36x - 9$ |
|
b
|
$4x - 9$ |
|
c
|
$36x - 4$ |
|
d
|
$24x - 9$ |
|
e
|
$36x - 1$ |
Expand
Using the distributive law, we multiply each term inside the parentheses by the number
$-5(x - 2y)=$
|
a
|
$5x - 10y$ |
|
b
|
$5x + 10y$ |
|
c
|
$-5x + 10y$ |
|
d
|
$-5x - 10y$ |
|
e
|
$5x - 7y$ |
$(x - 4)\cdot (-2)=$
|
a
|
$x-8$ |
|
b
|
$-6-2x$ |
|
c
|
$-8-2x$ |
|
d
|
$8+2x$ |
|
e
|
$8-2x$ |