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Chapter 7: Problem 75

Write an equivalent expression without parentheses. $$-(x-y)$$

Short Answer

Expert verified
-x + y

Step by step solution

01

Identify the expression inside the parentheses

The given expression is dash(x-ydash. The expression inside the parentheses is x-ydash.
02

Apply the negative sign

To remove the parentheses, distribute the negative sign dash1dash to both terms within the parentheses. This gives us: -1(x-y)=(-1)x+(-1)(-y)dash.
03

Simplify each term

Simplify the expression by multiplying the terms separately: -1(x)-(-1)y=-x+ydash.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property
The Distributive Property is a fundamental concept in algebra. It allows us to multiply a single term across terms inside parentheses. This can help simplify expressions and solve equations more easily. For instance, given an expression like a(b + c), using the Distributive Property, we can rewrite it as ab + ac. By 'distributing' the multiplication over addition or subtraction inside the parentheses, we ensure that each term is appropriately scaled before combining them.
Simplifying Expressions
Simplifying expressions means making them easier to work with by combining like terms and reducing complexity. Let's break it down with an example: Suppose you start with the expression 2x + 3x - y + 4y. Here, we can combine the 'x' terms and the 'y' terms. This gives us 5x + 3y. Simplifying expressions is like tidying up a room; we group similar items together to make everything clearer. This step is essential in problem-solving because simpler expressions are easier to manipulate and understand.
Negative Sign Distribution
Distributing a negative sign is crucial when dealing with parentheses. It鈥檚 essentially the Distributive Property with the multiplier being negative. For example, consider the expression -(x - y). To distribute the negative sign (-1) over the terms x and -y inside the parentheses, you perform the following:
  • First, multiply -1 by x, which gives -x.
  • Next, multiply -1 by -y, which results in +y.
So, -(x - y) becomes -x + y. We can simplify this distribution to make evaluating and working with our expressions more straightforward. Remembering to apply the negative sign to each term inside the parentheses helps prevent errors in more complex problems.

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Most popular questions from this chapter

Perform the indicated operations. Simplify, if possible. $$\frac{2 x+11}{x-3} \cdot \frac{3}{x+4}+\frac{-1}{4+x} \cdot \frac{6 x+3}{x-3}$$

For the first 50 mi of a 100 -mi trip, Liam drove \(40 \mathrm{mph} .\) What speed would he have to travel for the last half of the trip so that the average speed for the entire trip would be \(45 \mathrm{mph} ?\)

The length of a rectangular picture window is 3 yd greater than the width. The area of the rectangle is \(10 \mathrm{yd}^{2} .\) Find the perimeter.

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Solve for \(x:\) $$ x^{2}\left(1-\frac{2 p q}{x}\right)=\frac{2 p^{2} q^{3}-p q^{2} x}{-q} $$
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