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

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 expression combining • • numbers, possibly represented by symbols is an algebraic expression in the variable x ( x , y , S , T ,…) • • combined by any or all of the operations of addition, subtraction, multiplication, division, is an algebraic expression in the variables x and y exponentiation, and extraction of roots. • is not an algebraic expression: it is an equation.

5 6 A. Operations with algebraic expressions A. Operations with algebraic expressions Adding and subtracting algebraic expressions Multiplying algebraic expressions: distributive properties Example: Formulas: Example: This step mostly is not Method: written explicitly • Work out the brackets • Combine similar terms (terms that only differ by their numerical coefficients) 7 8 A. Operations with algebraic expressions A. Operations with algebraic expressions Multiplying algebraic expressions: special Multiplying algebraic expressions: product of products powers with the same base Square of a sum / difference: Example: Rule: product of powers with the same base Product of sum and difference: Exercise: Exercises: (1) (2)

9 10 A. Operations with algebraic expressions A. Operations with algebraic expressions Removing grouping symbols (brackets) Reference Example: 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) Method: (shortened in what follows as “handbook”) • Work out the brackets, from innermost towards the outside • Combine similar terms 11 12 A. Operations with algebraic expressions Handbook Chapter 0: Review of Algebra • 0.2 Some properties of Real Numbers B. Factoring • 0.4 Operations with Algebraic Expressions (except: Long Division, p17)

13 14 B. Factoring B. Factoring What is factoring? Method 1: factor out a common factor Writing an expression as a product of its Example: factors Example: (Check!) 15 16 B. Factoring B. Factoring Method 2: factor by grouping Method 3: special formulas Example: Square of a sum / difference: Product of sum and difference:

17 B. Factoring Handbook Chapter 0: Review of Algebra • 0.5 Factoring (Except: Factoring trinomials, p19)