A. Operations with algebraic Algebra practice part 1 expressions 3 - - PowerPoint PPT Presentation

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A. Operations with algebraic Algebra practice part 1 expressions 3 - - PowerPoint PPT Presentation

Jan 27, 2024 405 likes •462 views

1 2 A. Operations with algebraic Algebra practice part 1 expressions 3 4 A. Operations with algebraic expressions A. Operations with algebraic expressions What is an algebraic expression? What is an algebraic expression? Example: An

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Algebra practice part 1

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  • A. Operations with algebraic

expressions

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  • A. Operations with algebraic expressions

What is an algebraic expression? An expression combining

  • numbers, possibly represented by symbols

(x, y, S, T,…)

  • combined by any or all of the operations of

addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

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  • A. Operations with algebraic expressions

What is an algebraic expression? Example:

  • is an algebraic expression in the variable x
  • is an algebraic expression in the variables x and y
  • is not an algebraic expression: it is an equation.
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  • A. Operations with algebraic expressions

Adding and subtracting algebraic expressions Example: Method:

  • Work out the brackets
  • Combine similar terms (terms that only differ

by their numerical coefficients)

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  • A. Operations with algebraic expressions

Multiplying algebraic expressions: distributive properties Formulas: Example: This step mostly is not written explicitly

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  • A. Operations with algebraic expressions

Multiplying algebraic expressions: product of powers with the same base Example: Rule: product of powers with the same base Exercise:

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  • A. Operations with algebraic expressions

Multiplying algebraic expressions: special products Square of a sum / difference: Product of sum and difference: Exercises: (1) (2)

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  • A. Operations with algebraic expressions

Removing grouping symbols (brackets) Example: Method:

  • Work out the brackets, from innermost

towards the outside

  • Combine similar terms

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  • A. Operations with algebraic expressions

Reference E.F. Haeussler, R.S. Paul, R.J. Wood: Introductory Mathematical Analysis for Business, Economics and the Life and Social Sciences Prentice Hall (Thirteenth edition) (shortened in what follows as “handbook”)

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  • A. Operations with algebraic expressions

Handbook Chapter 0: Review of Algebra

  • 0.2 Some properties of Real Numbers
  • 0.4 Operations with Algebraic Expressions

(except: Long Division, p17)

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  • B. Factoring
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  • B. Factoring

What is factoring? Writing an expression as a product of its factors Example: (Check!)

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  • B. Factoring

Method 1: factor out a common factor Example:

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  • B. Factoring

Method 2: factor by grouping Example:

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  • B. Factoring

Method 3: special formulas Square of a sum / difference: Product of sum and difference:

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  • B. Factoring

Handbook Chapter 0: Review of Algebra

  • 0.5 Factoring

(Except: Factoring trinomials, p19)