Mathematics (2019) Grade(s): 8 - Grade 8 Accelerated

MA19.8A.5

Use the structure of an expression to identify ways to rewrite it. [Algebra I with Probability, 5]

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:
  • Properties of operations (including those in Appendix D, Table 1),
  • 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.
    For example, 3(x-5) = 3x-15 and 2a+12 = 2(a+6) or3a-a+10+2and x2-2x-15 = (x-5) (x+3).

Understanding

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

Vocabulary

  • like terms
  • Expression
  • Factor
  • properties of operations (Appendix D, Table 1)
  • Difference of squares
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