Expanding and Factoring

Equivalent Expressions

5 min

Problem

  1. Expand to write an equivalent expression: -12(-2x+4y)\text- \frac12(\text-2x+4y)
  2. Factor to write an equivalent expression: 26a−1026a -10

If you get stuck, use a diagram to organize your work.

Answer

Sample responses:

  1. x−2yx-2y
  2. 2(13a−5)2(13a-5)

Expressions equivalent to these are also acceptable, such as (13a−5)⋅2.(13a-5) \boldcdot 2.

Sample Response

Sample responses:

  1. x−2yx-2y
  2. 2(13a−5)2(13a-5)

Expressions equivalent to these are also acceptable, such as (13a−5)⋅2.(13a-5) \boldcdot 2.

Responding to Student Thinking
Points to Emphasizepoints_to_emphasize

Response: If students struggle with applying the distributive property to factor and expand expressions, plan to review this concept when opportunities arise over the next several lessons. For example, make sure to invite multiple students to share their thinking about the parentheses in this activity:

Standards
Addressing
  • 7.EE.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  • 7.EE.A.1·Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.