How Do You Distribute a Negative Sign When Squaring in Algebra?

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Homework Help Overview

The discussion revolves around the algebraic manipulation of an equation involving a square root and a negative sign. The original poster is attempting to solve the equation \(\sqrt{-3y-8} = -\sqrt{y+4}+2\) and is uncertain about how to properly distribute the negative sign when squaring both sides.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster questions how to correctly distribute the negative sign when squaring the right side of the equation. Some participants suggest alternative expressions to clarify the manipulation, while others provide a specific expansion of the squared term.

Discussion Status

The discussion is active, with participants providing clarifications and alternative formulations. There is a specific response that expands the squared term, indicating a productive direction in addressing the original poster's question.

Contextual Notes

The original poster is working within the constraints of algebraic rules and is seeking clarification on the proper handling of negative signs in the context of squaring expressions.

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Homework Statement



\sqrt{-3y-8} = -\sqrt{y+4}+2

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?
 
Last edited:
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If it's less confusing for you, you could write the righthand side as ##2-\sqrt{y+4}##.
 
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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!
 
To answer the question asked, squaring -\sqrt{y+ 4}+ 2 is (-\sqrt{y+ 4}+ 2)^2= y+ 4- 4\sqrt{y+ 4}+ 4.
 

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