7.8.4 Writing Equivalent Expressions

Algebra 17.8.4 Writing Equivalent Expressions

Search for key terms or text.

Cool Down

Draw a diagram to show that $(3 x + 1) (x + 2)$ is equivalent to $3 x^{2} + 7 x + 2$ .

Compare your answer:

Diagram should show partial products of $3 x (x)$ , $6 x$ , $x$ , and 2, which add up to $3 x^{2} + 7 x + 2$ .

An area model using a rectangle is divided into 4 smaller rectangles with both vertical and horizontal segments. The top left section of the rectangle is labeled x and the top right section of the rectangle is labeled 2. The top left side length of the rectangle is labeled 3 times x and the bottom left side length of the rectangle is labeled 1. There are four areas inside the rectangle: The top left area that is bordered by x and 3x is labled 3 times x squared. The top right area under the 2 is labeled 6 times x. In the bottom row, the left region is labeled x and the right region is labeled 2.

Is $(x + 4)^{2}$ equivalent to $2 x^{2} + 8 x + 8$ ? Explain or show your reasoning.

Compare your answer:

No. $(x + 4) (x + 4) = x^{2} + 4 x + 4 x + 16 = x^{2} + 8 x + 16$ .

Why Should I Care?

Illustration of a vibrant pumpkin patch with scattered pumpkins, a wheelbarrow, and a "Pumpkin" sign. In the background, barns and a windmill stand under cloudy skies.

Anna's class entered a contest where they had to build a catapault and use it to launch a pumpkin at a distant target. But when Anna's class shot their pumpkin for the first time, it went wildly off course.

Anna thought about their problem and came up with a solution. If Anna's class used a quadratic equation, they could mathematically find the best place and angle for their pumpkin catapault. It worked! Their accuracy went from 2% to 99%.

You can use quadratic equations for any object that travels in a curved path, like footballs, frisbees, and golf balls.

Previous Next

Citation/Attribution

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License and you must attribute OpenStax.

Attribution information

If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course
If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:
Access for free at https://openstax.org/books/algebra-1/pages/about-this-course

Citation information

Use the information below to generate a citation. We recommend using a citation tool such as this one.
- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/7-8-4-writing-equivalent-expressions

© May 21, 2025 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.