Distributing a Negative Sign

In summary, distributing a negative sign is a mathematical operation that simplifies equations involving negative numbers and maintains the rules of algebra. To distribute a negative sign, multiply it to each term within parentheses. This can also be applied to a single term by writing it as (-1) multiplied by that term. When distributing a negative sign to a negative term, it results in a positive term. However, there are exceptions, such as when there is a subtraction sign before parentheses, in which case the operation inside the parentheses changes to addition.
  • #1
Drakkith
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Homework Statement



[itex]\sqrt{-3y-8}[/itex] = [itex]-\sqrt{y+4}+2[/itex]

I need to square both sides in order to solve for Y.
But, how do I distribute the negative sign on the right side? Would it be similar to (-x+2)2 or -(x+2)2?
 
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  • #2
If it's less confusing for you, you could write the righthand side as ##2-\sqrt{y+4}##.
 
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  • #3
vela said:
If it's less confusing for you, you could write the righthand side as ##2-\sqrt{y+4}##.

Oh, well that makes perfect sense now. Thanks!
 
  • #4
To answer the question asked, squaring [itex]-\sqrt{y+ 4}+ 2[/itex] is [itex](-\sqrt{y+ 4}+ 2)^2= y+ 4- 4\sqrt{y+ 4}+ 4[/itex].
 

What is the purpose of distributing a negative sign?

Distributing a negative sign is a mathematical operation that allows us to simplify and solve equations involving negative numbers more easily. It also helps to maintain the rules of algebra and ensure the accuracy of our calculations.

How do I distribute a negative sign?

To distribute a negative sign, you simply multiply it to each term within the parentheses. For example, if you have -3(x + 5), you would distribute the negative sign by multiplying -3 to both x and 5, resulting in -3x - 15.

Can I distribute a negative sign to a single term?

Yes, you can distribute a negative sign to a single term by writing it as (-1) multiplied by that term. For instance, -2x can be written as (-1)(2x) which can then be distributed to result in -2x.

What happens when I distribute a negative sign to a negative term?

When you distribute a negative sign to a negative term, it results in a positive term. For example, -3(-x) becomes 3x.

Are there any exceptions to distributing a negative sign?

Yes, there are some cases where distributing a negative sign does not apply. One example is when there is a subtraction sign before the parentheses. In this case, the negative sign is distributed by changing the operation inside the parentheses to addition. For example, -2(x - 5) becomes -2x + 10.

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