# Lesson 19

Expanding and Factoring

### Lesson Narrative

In grade 6, students worked extensively with the distributive property involving both addition and subtraction, but only with positive coefficients. In the previous lesson, students learned to rewrite subtraction as "adding the opposite" to avoid common pitfalls. In this lesson, students practice using the distributive property to write equivalent expressions when there are rational coefficients. Some of the expressions they will work with are in preparation for understanding combining like terms in terms of the distributive property, coming up in the next lesson. (For example, $$17a-13a$$ can be rewritten $$a(17-13)$$ using the distributive property, so it is equivalent to $$a \boldcdot 4$$ or $$4a.$$

### Learning Goals

Teacher Facing

• Apply the distributive property to expand or factor an expression that includes negative coefficients, and explain (orally and using other representations) the reasoning.
• Comprehend the terms “expand” and “factor” (in spoken and written language) in relation to the distributive property.

### Student Facing

Let's use the distributive property to write expressions in different ways.

### Student Facing

• I can organize my work when I use the distributive property.
• I can use the distributive property to rewrite expressions with positive and negative numbers.
• I understand that factoring and expanding are words used to describe using the distributive property to write equivalent expressions.

Building On

Building Towards

### Glossary Entries

• expand

To expand an expression, we use the distributive property to rewrite a product as a sum. The new expression is equivalent to the original expression.

For example, we can expand the expression $$5(4x+7)$$ to get the equivalent expression $$20x + 35$$.

• factor (an expression)

To factor an expression, we use the distributive property to rewrite a sum as a product. The new expression is equivalent to the original expression.

For example, we can factor the expression $$20x + 35$$ to get the equivalent expression $$5(4x+7)$$.

• term

A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. For example, the expression $$5x + 18$$ has two terms. The first term is $$5x$$ and the second term is 18.