Let's think about how to simplify the following expression:
In this example, we're subtracting the entire group of terms in parentheses from In such cases, we distribute the negative sign to each term in the parentheses first and then simplify by collecting like terms.
Removing the parentheses by distributing the negative sign, we get
Finally, we collect like terms:
Let's take a look at another example.
Simplify the expression
First, we remove the parentheses by distributing the negative sign. This gives
Finally, we collect like terms:
$5-(x+1)=$
|
a
|
$-4+x$ |
|
b
|
$4-x$ |
|
c
|
$6+x$ |
|
d
|
$6-x$ |
|
e
|
$4+x$ |
$-6-(2x+4)=$
|
a
|
$-2+2x$ |
|
b
|
$-10-2x$ |
|
c
|
$-8-x$ |
|
d
|
$-2-2x$ |
|
e
|
$-10+2x$ |
Simplify the expression
First, we remove the parentheses by distributing the negative sign. This gives
Finally, we collect like terms:
Simplify the expression $4-(2h-3).$
|
a
|
$7+2h$ |
|
b
|
$2+2h$ |
|
c
|
$1+2h$ |
|
d
|
$1-2h$ |
|
e
|
$7-2h$ |
Simplify the expression $-3h-(2h-9).$
|
a
|
$-h-9$ |
|
b
|
$h-9$ |
|
c
|
$-h+9$ |
|
d
|
$-5h+9$ |
|
e
|
$-5h-9$ |
Sometimes, to subtract a group of terms, we have to apply the distributive law.
For example, let's simplify the following expression:
First, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.
Next, we expand the expression inside the brackets using the distributive law. This gives
Now, we proceed as before. Removing the brackets by distributing the negative sign gives
Finally, we collect like terms:
Simplify the expression
Notice that the expression we need to subtract from must be expanded using the distributive law.
So first, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.
Next, we expand the expression inside the brackets using the distributive law. This gives
Now, we remove the brackets by distributing the negative sign. This gives
Finally, we collect like terms:
$5-3(x+1)=$
|
a
|
$2-3x$ |
|
b
|
$6-x$ |
|
c
|
$6-3x$ |
|
d
|
$2-x$ |
|
e
|
$2+3x$ |
$-6 - 2(3t + 5)=$
|
a
|
$4 - 6t$ |
|
b
|
$-16 - 6t$ |
|
c
|
$-4 - 6t$ |
|
d
|
$-16 + 6t$ |
|
e
|
$16 + 6t$ |
Simplify the expression
Notice that the expression we need to subtract from must be expanded using the distributive law.
So first, let's write some big brackets around the expression in parentheses, keeping the minus sign outside.
Next, we expand the expression inside the brackets using the distributive law. This gives
Now, we remove the brackets by distributing the negative sign. This gives
Finally, we collect like terms:
$4-6(2h-3)=$
|
a
|
$22 - 12h $ |
|
b
|
$-4h+6$ |
|
c
|
$12h-18$ |
|
d
|
$20h+18$ |
|
e
|
$4h-6$ |
$-1-5(2v-1)=$
|
a
|
$4-5v$ |
|
b
|
$2-10v$ |
|
c
|
$2-12v$ |
|
d
|
$-1-5v$ |
|
e
|
$4-10v$ |