Mathematics (2019) Grade(s): 09-12 - Algebra I with Probability

MA19.A1.5

Use the structure of an expression to identify ways to rewrite it.

COS Examples

Example: See $x^4 - y^4$ as $(x^2)^2 - (y^2)^2$, thus recognizing it as a difference of squares that can be factored as $(x^2 - y^2)(x^2 + y^2)$.

Unpacked Content

Knowledge

Students know:
  • Algebraic properties.
  • When one form of an algebraic expression is more useful than an equivalent form of that same expression.

Skills

Students are able to:
  • Use algebraic properties to produce equivalent forms of the same expression by recognizing underlying mathematical structures.

Understanding

Students understand that:
  • Generating equivalent algebraic expressions facilitates the investigation of more complex algebraic expressions.

Vocabulary

  • Terms
  • Linear expressions
  • Equivalent expressions
  • Difference of two squares
  • Factor
  • Difference of squares
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