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6.2

Activity

Using Diagrams to Understand Equivalent Expressions

Standards Alignment

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Addressing

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Compare the diagram that shows and the partially completed diagram for to determine the values of and .

What does the bottom right corner tell you about the connection between the constant term, 8, and the missing parts of the factors, and ?
What is the connection between the linear term, , and the two sections of the diagram with the underlines? How is that connected to and ?
Find values for and , and rewrite in factored form.
Rewrite these quadratic expressions in factored form. As you work, consider how the values of the constant and linear terms help decide the values of and .

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6.3

Activity

Let’s Rewrite Some Expressions!

Standards Alignment

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Addressing

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Each row in the table contains a pair of equivalent expressions.

Complete the table with the missing expressions. If you get stuck, consider drawing a diagram.

factored form	standard form

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Student Lesson Summary

Previously, you learned how to expand a quadratic expression in factored form and write it in standard form by applying the distributive property.

For example, to expand , we apply the distributive property to multiply by and 4 by . Then, we apply the property again to multiply by , by 5, 4 by , and 4 by 5.

To keep track of all the products, we could make a diagram like this:

Next, we could write the products of each pair inside the spaces:

The diagram helps us see that is equivalent to , or in standard form, .

The linear term, or the term with a single factor of in the standard form of a quadratic expression, is and has a coefficient of 9, which is the sum of 5 and 4.
The constant term, 20, is the product of 5 and 4.

We can use these observations to reason in the other direction: starting with an expression in standard form and writing it in factored form.

For example, suppose we wish to write in factored form.

Let’s start by creating a diagram and writing in the terms and 24.

We need to think of two numbers that multiply to make 24 and add up to -11.

After some thinking, we see that -8 and -3 meet these conditions. The product of -8 and -3 is 24. The sum of -8 and -3 is -11.

So, written in factored form is .

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Lesson 6

Rewriting Quadratic Expressions in Factored Form (Part 1)

Warm-up

Puzzles of Rectangles

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Activity

Using Diagrams to Understand Equivalent Expressions

Standards Alignment

A-REI.4.b

Are You Ready for More?

Activity

Let’s Rewrite Some Expressions!

Standards Alignment

A-SSE.2

A-REI.4.b

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Student Lesson Summary

Glossary

linear term

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Standards Alignment

6.G.1

A-REI.4.b

A-SSE.2

A-SSE.3.a

A-SSE.3.a