Simplifying Expressions Lesson

by Felix Gabathuler

| 35 QuestionsToday we are going to make sure that everyone is on the same page when thinking about Algebra! Yay! Scroll through this document and complete the each section as directed. Watch the videos, fill in the blanks, and really concentrate!

You should take notes on what you learn today! I will be checking to see how convincing your work is in your notebooks!

Algebra is the language through which we describe patterns. It's like a way of writing really long patterns that go on forever as something much smaller. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject.

In simple addition, what you did in elementary school, we learned to add all the numbers together to get a sum. In Pre-Algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers. Can you figure out the pattern below?

The pattern above increases by 4 every time you increase position by 1. We're going to get into the patterns and how to figure them out later. First, we've got to cover the basics. Watch the video below to understand what a variable is and how we can combine like terms.

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After watching the video, write down how you would explain the concept of a variable to someone who has never heard about that before. Use 1 example.

Now, Let's solidify our combining like terms practice with a few extra questions! Make sure to write your answers properly, doodloodloodloo... (pinkie finger waving), by always writing the term with the variable first. Complete the following questions that have blue bubbles next to them.

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Type your answers here without using spaces.

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Are the following expressions equivalent? Explain your reasoning.

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Write an expression in simplest form that represents the area of the banner.

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Draw a diagram that shows how the expression can represent the area of a figure. Then simplify the expression.

Now, watch this short video on distribution, which will help you combine like terms in bigger expressions

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How would you explain "distribution" to someone who doesn't know? Can you come up with a real world example?

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Simplify the following expression using distribution: 2(y - 8)

-2y + 16

2y - 16

8y - 2

2y + 16

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Simplify the following expression using distribution: -5(2x + 1)

-10x + 5

10x - 5

-10x - 5

10x + 5

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Which of the following choices could be the non-simplified version of: 3x - 5 There might be more than one answer!

3(x-4)

3(x - 1) - 2

2 + 3x - 7

9x - 2(3x + 3) + 1

3x - 6x - 5

Things are a little different when you have more than one parentheses in your expression. Check out this video to learn how to distribute using a negative number and what happen when you are dealing with a really big expression!

Let's practice a few more distribution problems! Only answer the questions with the blue bubbles, keep things proper, and simplify!

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Type your answers here without using spaces.

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Sometimes you will see expressions that have more than one pair of parentheses! Instead of crying, watch this short video to see how you can simplify those.

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In your own words, explain the steps to simplify the expression: 3(2x + 1) + 4(5x + 3) . You do not need to solve the problem. Just write what you would do first, second, third, etc.

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Extension!

You apply gold foil to a piece of red poster board to make the design shown below.

Write an expression in simplest form that represents the area of the gold foil.

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