/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 60 Simplify each expression as comp... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 60

Simplify each expression as completely as possible. $$5(y-3)+2[y-5(3-y)]$$

Short Answer

Expert verified
17y - 45

Step by step solution

01

- Distribute within the parentheses

First, distribute the constants inside each set of parentheses. For the first term, distribute the 5: \[5(y-3) = 5y - 15\]For the second term, distribute the -5 inside the parentheses: \[5(3-y) = 15 - 5y\] which gives us:\[2[y - (15-5y)]\]
02

- Simplify inside the brackets

Next, combine like terms inside the brackets. Within the brackets, we have: \[y - 15 + 5y\] Combine the like terms to get:\[6y - 15\]
03

- Distribute the 2 across the terms

Distribute the 2 to both terms inside the brackets: \[2(6y - 15) = 12y - 30\]
04

- Combine all like terms

Now, we have the expression simplified to: \[5y - 15 + 12y - 30\]. Combine the like terms to get the final simplified form: \[17y - 45\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Distribution
When simplifying algebraic expressions, distribution helps in expanding terms within parentheses. It involves multiplying a single term by each term inside the parentheses. For example, in the expression \(5(y-3)\), we distribute the 5 to both \(y\) and -3, resulting in \(5y - 15\). This technique ensures that each term is properly accounted for before moving on to the next steps of simplification.
Combining Like Terms
Combining like terms is a crucial step in simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. In our example, after distributing, we get terms like \(5y\) and -15. Later, with additional operations, we obtain more like terms such as \(12y\) and -30. We combine the terms \(5y\) and \(12y\) to get \(17y\), and -15 and -30 to yield -45. This process reduces the expression to a simpler form.
Parentheses
Understanding the role of parentheses in algebra is key for simplification. Parentheses indicate the terms that need to be considered together, often requiring distribution and then combining like terms. In the given expression, the parentheses in \(5(y-3)\) group \(y\) and -3, guiding us to distribute 5 across both terms. Similarly, the expression \[2[y - 5(3-y)]\] requires inner distribution first, followed by outer. Removing parentheses systematically helps in breaking down complex expressions into simpler parts.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$3 a^{2} b+a b^{2}-a b^{2}-2 a^{2} b-a b^{2}$$

Simplify by combining like terms whenever possible. $$0.8 x-5-x+2.7$$

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$y(x-z)^{2}$$

Simplify by combining like terms whenever possible. $$y^{2}-6 y+y^{2}-y$$

Simplify each expression as completely as possible. $$-a^{2}(3 a-7)-2 a\left[a^{2}-4(a-2)\right]$$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.