To simplify an expression like , we need to distribute the negative sign across each of the terms inside the parentheses. This can be accomplished by treating the negative sign like multiplication by For example:
In these cases, the negative sign in front of the parentheses represents the . However, to save space, only the negative sign is shown.
Simplify the expression
First, we rewrite the negative sign as multiplication by
Then, we distribute the to each term in the parentheses, and simplify:
Expand $-\left(y + 7z\right).$
|
a
|
$-y - 7z$ |
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b
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$y + 7z$ |
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c
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$7 y + z$ |
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d
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$-y + 7z$ |
|
e
|
$y - 7z$ |
Expand $-\left( \dfrac{1}{2} + 3c \right).$
|
a
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$-\dfrac{1}{2} + 3c$ |
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b
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$\dfrac{1}{2} + 3c$ |
|
c
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$\dfrac{1}{2} - 3c$ |
|
d
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$-\dfrac{1}{2} - 3c$ |
|
e
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$3 + \dfrac{1}{2} c$ |
Simplify the expression
First, we rewrite the negative sign as multiplication by
Then, we distribute the to each term in the parentheses, and simplify:
Simplify $-(0.3x-0.2y).$
|
a
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$-0.3x-0.2y$ |
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b
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$0.3x+0.2y$ |
|
c
|
$-0.3x+0.2y$ |
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d
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$-0.2x-0.4y$ |
|
e
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$0.3x-0.2y$ |
Simplify $-(a-2 b).$
|
a
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$-a+2b$ |
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b
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$2a+b$ |
|
c
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$-a-2b$ |
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d
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$a+2b$ |
|
e
|
$a-b$ |
By distributing the negative sign across each of the terms inside the parentheses, we're merely changing the sign of each term. In other words:
If a term was positive inside the parentheses, it becomes negative.
If a term was negative inside the parentheses, it becomes positive.
Simplify
To distribute the negative sign to the terms inside the parentheses, all we have to do is change the sign of each term.
Simplify the expression $-(10j-11k+15m).$
|
a
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$10j+11k+15m$ |
|
b
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$-10j-11k-15m$ |
|
c
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$-10j+11k-15m$ |
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d
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$10j+11k-15m$ |
|
e
|
$-10j+11k+15m$ |
Simplify $-(-a+b-c).$
|
a
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$a-b+c$ |
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b
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$-a+b-c$ |
|
c
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$a-b-c$ |
|
d
|
$-a-b-c$ |
|
e
|
$a+b+c$ |