Problem 129 - Introductory Algebra for College Students

Question

Explain how to simplify an algebraic expression in which a negative sign precedes parentheses.

Step-by-Step Solution

Answer

To simplify an algebraic expression with a negative sign preceding parentheses, apply the distributive property by multiplying every term inside the parentheses by -1. For example, `-(a - b + c)` simplifies to `-a + b - c`. If any further simplifications can be made, such as combining like terms, do these next.

Step 1: Identify The Negative Sign Preceding Parentheses

The first step is to identify the negative sign just before the parentheses. This means that every term inside the parentheses will be multiplied by -1. If the expression is `- (a - b + c)`, the -1 will be distributed to each term inside the parentheses.

Step 2: Distribute The Negative Sign

Apply the distributive property by multiplying every term inside the parentheses by -1. `-(a - b + c)` will become `-a + b - c`. Here, you've distributed the negative sign to `a` which becomes `-a`, `b` becomes `+b` or `b` and `c` becomes `-c`.

Step 3: Simplify Further If Necessary

If there are like terms or any further simplifications that can be done, go ahead and do those. In this case `-a + b - c` is already in its simplest form. If there are any coefficients outside the parentheses such as `-2(a - b + c)`, distribute as `-2*a + 2*b - 2*c`.